# exterior angles of a pentagon

Since one of the five angles is 180, it means that this is not a pentagon. Practice: Angles of a polygon. For our equilateral triangle, the exterior angle of any vertex is 120°. So let's think about that as a negative angle measure. Subsequently, question is, do all polygons add up to 360? Sophia partners One important property about exterior angles of a regular polygon is that, the sum of the measures of the exterior angles of a polygon is always 360°. We know any interior angle is 150°, so the exterior angle is: Look carefully at the three exterior angles we used in our examples: Prepare to be amazed. So five corners, which means a pentagon. Properties. Sum of the exterior angles of a polygon. So each exterior angle is 360 divided by the n, the number of sides. The marked angles are called the exterior angles of the pentagon. Therefore our formula holds even for concave polygons. Still, this is an easy idea to remember: no matter how fussy and multi-sided the regular polygon gets, the sum of its exterior angles is always 360°. So each interior angle = 180–72 = 108 deg. Together, the adjacent interior and exterior angles will add to 180°. of the polygon. Geometric solids (3D shapes) Video transcript. Q. Suppose, for instance, you want to know what all those interior angles add up to, in degrees? After working your way through this lesson and the video, you learned to: Get better grades with tutoring from top-rated private tutors. Control the size of a colored exterior angle by using the slider with matching color. On top of the courtyard, we will superimpose a concave decagon (just as a decade has 10 years, a decagon has 10 sides). The sum of the exterior angles of a polygon is 360°. If you prefer a formula, subtract the interior angle from 180°: What do we have left in our collection of regular polygons? The new formula looks very much like the old formula: Again, test it for the equilateral triangle: Hey! * The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 33 of Sophia’s online courses. 299 Let's find the sum of the interior angles, as well as one interior angle: Every regular polygon has exterior angles. this means there are 5 exterior angles. Click hereto get an answer to your question ️ Write the measurements of exterior and interior angles of regular pentagon(i) in degrees(ii) in radian Next lesson. The formula for the sum of that polygon's interior angles is refreshingly simple. Therefore. The interior and exterior angles of a polygon are different for different types of polygons. So it doesn't seem to be exterior. Tracing all the way around the polygon makes one full turn, so the sum of the exterior angles must be 360°. Exterior Angles Of A Polygon - Displaying top 8 worksheets found for this concept. The regular polygon with the fewest sides -- three -- is the equilateral triangle. If you pay very careful attention to the direction you are facing in the video, you can verify that at vertex H, you turn through the direction you were facing when you started at vertex A. Triangles are easy. That is a common misunderstanding. The sum of all the exterior angles in a polygon is equal to 360 degrees. Evidence for this is that you finish at vertex J facing the same direction you started-northeast. Please try another device or upgrade your browser. Below is a satellite image of the courtyard of my workplace-Normandale Community College. sures greater than 180°, but the negative exterior angle brings the total down to 180°. The sum of the internal angle and the external angle on the same vertex is 180°. And if it doesn't hold for pentagons, then it doesn't hold for other figures and our formula is more limited than we thought. Divide the total possible angle by 5 to determine the value of one interior angle. Exterior Angles of Polygons: A Quick (Dynamic and Modifiable) Investigation and Discovery. Many different colleges and universities consider ACE CREDIT recommendations in determining the applicability to their course and degree programs. To find the measure of the interior angle of a pentagon, we just need to use this formula. The formula for calculating the size of an exterior angle is: exterior angle of a polygon = 360 ÷ number of sides. They are formed on the outside or exterior of the polygon. Polygons are like the little houses of two-dimensional geometry world. The number of sides in a polygon is equal to the number of angles formed in a particular polygon. The interior angle of regular polygon can be defined as an angle inside a shape and calculated by dividing the sum of all interior angles by the number of congruent sides of a regular polygon is calculated using Interior angle of regular polygon=((Number of sides-2)*180)/Number of sides.To calculate Interior angle of regular polygon, you need Number of sides (n). credit transfer. We still have. Square? 37 The sum of the exterior angles of a … But the exterior angles sum to 360°. Therefore, for all equiangular polygons, the measure of one exterior angle is equal to 360 divided by the number of sides in the polygon. For a polygon to be a regular polygon, it must fulfill these four requirements: Regular polygons exist without limit (theoretically), but as you get more and more sides, the polygon looks more and more like a circle. Then I resolve the problems by adapting the argument slightly so that we can be sure it applies to all polygons. Measure of each exterior angle = 360°/n = 360°/3 = 120° Exterior angle of a Pentagon: n = 5. Since you are extending a side of the polygon, that exterior angle must necessarily be supplementary to the polygon's interior angle. The interior angle is one of the vertices of the polygon. They don't appear to be supplementary. Properties Of Exterior Angles Of a Polygon If you pay very careful attention to the direction you are facing in the video, you can verify that at vertex H, you turn. To find the size of each angle, divide the sum, 540º, by the number of angles in the pentagon. So the two angles do not seem to add to 180°. The sum of exterior angles in a polygon is always equal to 360 degrees. So the premise of the question is false. The sum of an interior angle and its corresponding exterior angle is always 180 degrees since they lie on the same straight line. The Exterior Angles of a Polygon add up to 360° © 2015 MathsIsFun.com v 0.9 In other words the exterior angles add up to one full revolution. The argument goes smoothly enough when the polygon is convex. Some of the worksheets for this concept are Interior and exterior angles of polygons, Interior angles of polygons and multiple choices, 6 polygons and angles, Infinite geometry, Work 1 revised convex polygons, 15 polygons mep y8 practice book b, 4 the exterior angle theorem, Mathematics linear 1ma0 angles polygons. For instance, in an equilateral triangle, the exterior angle is not 360° - 60° = 300°, as if we were rotating from one side all the way around the vertex to the other side. Regular polygons have as many interior angles as they have sides, so the triangle has three sides and three interior angles. After working through all that, now you are able to define a regular polygon, measure one interior angle of any polygon, and identify and apply the formula used to find the sum of interior angles of a regular polygon. Do you see why it's a problem? This fixes our two problems: Therefore our formula holds even for concave polygons. since they all have to add to 360 you can divide 360/5 = 72. As a demonstration of this, drag any vertex towards the center of the polygon. So we need to subtract that from the 900° total, leaving 540° for the interior angles of the pentagon. Polygons Interior and Exterior Angles Of Polygons Investigation Activity And Assignment This is an activity designed to lead students to the formulas for: 1) one interior angle of a regular polygon 2)the interior angle sum of a regular polygon 3)one exterior angle of a regular polygon 4)the exteri The sum of exterior angles in a polygon is always equal to 360 degrees. Press Play button to see. Likewise, a square (a regular quadrilateral) adds to 360° because a square can be divided into two triangles. And if we don't have 5 pairs of 180°, then the formula 5*180-360 doesn't hold. There is nothing special about this being a pentagon. guarantee You can measure interior angles and exterior angles. Regular Polygon : A regular polygon has sides of equal length, and all its interior and exterior angles are of same measure. So the angles are 36, 72, 108, 144, 180. Interior angles of a Regular Polygon = [180°(n) – 360°] / n. Method 2: If the exterior angle of a polygon is given, then the formula to find the interior angle is. Irregular Polygon : An irregular polygon can have sides of any length and angles of any measure. SOPHIA is a registered trademark of SOPHIA Learning, LLC. Now it is time to take a closer look at the exterior angles and study the concept of exterior angles of a polygon. (which is the same as the number of sides). The negative angle measure at vertex J essentially undoes all of the extra turning at vertices H and I. Exterior angles of a polygon have several unique properties. A concave polygon, informally, is one that has a dent. The measures of the interior and exterior angle now add up to 180° again. Each exterior angle is paired with a corresponding interior angle, and each of these pairs sums to 180° (they are supplementary). If it is a Regular Polygon (all sides are equal, all angles are equal) Shape Sides Sum of Interior Angles Shape Each Angle; Triangle: 3: 180° 60° Quadrilateral: 4: 360° 90° Pentagon: 5: 540° 108° Hexagon: 6: 720° 120° Heptagon (or Septagon) 7: 900° 128.57...° Octagon: 8: 1080° 135° Nonagon: 9: 1260° 140°..... Any Polygon: n (n−2) × 180° (n−2) × 180° / n Yes, but we can look at it a different way. exterior angles Angles 1, 2, 7, and 8 are exterior angles. Video does not play in this browser or device. Or can we fix things up so that it applies to concave polygons also? And it works every time. What is the … One interior angle of a pentagon has a measure of 120 degrees. Here is the formula: You can do this. An exterior angle of a polygonis an angleat a vertexof the polygon, outside the polygon, formed by one side and the extension of an adjacent side. So it doesn't seem to be, Below is a satellite image of the courtyard of my workplace-, The turn at each vertex corresponds to the exterior angle at that vertex, and. But that was an illustration -- it's wrong! Every time you add up (or multiply, which is fast addition) the sums of exterior angles of any regular polygon, you, Enclose a space, creating an interior and exterior, Have all sides equal in length to one another, and all interior angles equal in measure to one another, Identify and apply the formula used to find the sum of interior angles of a regular polygon, Measure one interior angle of a polygon using that same formula, Explain how you find the measure of any exterior angle of a regular polygon, Know the sum of the exterior angles of every regular polygon. Notice that corresponding interior and exterior angles are supplementary (add to 180°). Measure of a Single Exterior Angle Formula to find 1 angle of a regular convex polygon of n … You turn the other way. That dodecagon! The exterior angles of this pentagon are formed by extending its adjacent sides. Together, the adjacent interior and exterior angles will add to 180°. Learn faster with a math tutor. Get help fast. A polygon is a flat figure that is made up of three or more line segments and is enclosed. The exterior angle of a polygon is the angle between a side, and the extension of the side next to it. 180 - 108 = 72° THE SUM OF (five) EXTERIOR ANGLES OF A PENTAGON is 72 × 5 = 360°. For a regular polygon, the total described above is spread evenly among all the interior angles, since they all have the same values. A series of images and videos raises questions about the formula n*180-360 describing the interior angle sum of a polygon, and then resolves these questions. [(n - 2 ) 180] / n The regular polygon with the most sides commonly used in geometry classes is probably the dodecagon, or 12-gon, with 12 sides and 12 interior angles: Pretty fancy, isn't it? The exterior angle of a regular polygon = 72 deg. 1 2 Since the pentagon is a regular pentagon, the measure of each interior angle will be the same. You will see that the angles combine to a full 360° circle. In the figure or pentagon above, we use a to represent the interior angle of the pentagon and we use x,y,z,v, and w to represents the 5 exterior angles. For a square, the exterior angle is 90°. As you walk, pay attention to two things: The walk begins at vertex A and ends at vertex J. Exterior angle of a triangle: For a triangle, n = 3. Regular Polygon : A regular polygon has sides of equal length, and all its interior and exterior angles are of same measure. These pairs total 5*180=900°. Examples. There is one exterior angle that is not marked. Interior angle of polygons. Although you know that sum of the exterior angles is 360, you can only use formula to find a single exterior angle if the polygon is regular! We already know that the sum of the interior angles of a triangle add up to 180 degrees. The question asked about the exterior angles, not the interior angles. Multiply each of those measurements times the number of sides of the regular polygon: It looks like magic, but the geometric reason for this is actually simple: to move around these shapes, you are making one complete rotation, or turn, of 360°. Interior Angle of a polygon = 180° – Exterior angle of a polygon. In the figure, angles 1, 2, 3, 4 and 5 are the exterior angles of the polygon. This page includes a lesson covering 'the exterior angles of a polygon' as well as a 15-question worksheet, which is printable, editable, and sendable. Each exterior angle is paired with a corresponding interior angle, and each of these pairs sums to 180° (they are supplementary). But just because it has all those sides and interior angles, do not think you cannot figure out a lot about our dodecagon. The sum of the measures of the exterior angles is still 360°. Move the vertices of these polygons anywhere you'd like. Ans- The interior angles are constituted by covering the angular vertices, which are inside the sides of a pentagon. In the video below, you join me on a walk around the courtyard. What about a concave polygon? Remember what the 12-sided dodecagon looks like? The sum of the interior angles = 5*108 = 540 deg. For our equilateral triangle, the exterior angle of any vertex is 120°. You also can explain to someone else how to find the measure of the exterior angles of a regular polygon, and you know the sum of exterior angles of every regular polygon. A pentagon has 5 interior angles, so it has 5 interior-exterior angle pairs. The sum of all the internal angles of a simple polygon is 180(n–2)° where n is the number of sides.The formula can be proved using mathematical induction and starting with a triangle for which the angle sum is 180°, then replacing one side with two sides connected at a vertex, and so on. Notice what happens at vertex J. The interior angle mea. Each interior angle of a pentagon is 108 degrees. The sum of the angles of the interior angles in the case of a triangle is 180 degrees, whereas the sum of the exterior angles is 360 degrees. The exterior angle is 180 - interior angle. The interior angle of a polygon is an angle formed inside a polygon and it is between two sides of a polygon. You can also add up the sums of all interior angles, and the sums of all exterior angles, of regular polygons. Exterior angles of a polygon have several unique properties. Tracing around a convex n-gon, the angle "turned" at a corner is the exterior or external angle. The measure of each interior angle of an equiangular n -gon is. Something is different at vertex J...what is it? The exterior angle appears to lie inside of the pentagon. For a square, the exterior angle is 90°. The size of each interior angle of a polygon is given by; Measure of each interior angle = 180° * (n – 2)/n Method 3: Sofor example the interior angles of a pentagon always add up to 540°, so in a regular pentagon (5 sides), each one is one fifth of that, or 108°.Or, as a formula, each interior angle of a regular polygon is given by:180(n−2)n degreeswheren is the number of sides You turn at vertices I and J, so it all adds up to more than 360°, right? The exterior angles of a triangle, quadrilateral, and pentagon are shown, respectively, in the applets below. Try it first with our equilateral triangle: To find the measure of a single interior angle, then, you simply take that total for all the angles and divide it by n, the number of sides or angles in the regular polygon. The word "polygon" means "many angles," though most people seem to notice the sides more than they notice the angles, so they created words like "quadrilateral," which means "four sides.". Angles 1 and 8 and angles 2 and 7 are alternate exterior angles. The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360°. One of the standard arguments for the formula for the sum of the interior angles of a polygon involves the exterior angles of the polygon. © 2021 SOPHIA Learning, LLC. Can you find the exterior angle of this concave pentagon? So...does our formula apply only to convex polygons? Our formula works on triangles, squares, pentagons, hexagons, quadrilaterals, octagons and more. As a demonstration of this, drag any vertex towards the center of the polygon. Some additional information: The polygon has 360/72 = 5 sides, each side = s. It is a regular pentagon. The sum of exterior angles in a polygon is always equal to 360 degrees. Exterior angles of a polygon are formed when by one of its side and extending the other side. Exterior angle – The exterior angle is the supplementary angle to the interior angle. In what follows, I present the basic argument quickly and then describe how and why the argument becomes problematic when the polygon is concave. The sum of exterior angles of a polygon is 360°. It works! Exercise worksheet on 'The exterior angles of a polygon.' Interior and Exterior Angles of a Polygon. These pairs total 5*180=900°. Therefore, for all equiangular polygons, the measure of one exterior angle is equal to 360 divided by the number of sides in the polygon. Want to see the math tutors near you? These are not the reflex angle (greater than 180°) created by rotating from the exterior of one side to the next. Some additional information: The polygon has 360/72 = 5 sides, each side = s. It is a regular pentagon. Each interior angle of a regular polygon = n 1 8 0 o (n − 2) where n = number of sides of polygon Each exterior angle of a regular polygon = n 3 6 0 o According to question, n 3 6 0 o … Therefore, for all equiangular polygons, the measure of one exterior angle is equal to 360 divided by the number of sides in the polygon. A pentagon has 5 interior angles, so it has 5 interior-exterior angle pairs. But the exterior angles sum to 360°. Find a tutor locally or online. More formally, a concave polygon has at least one interior angle greater than 180°. Exterior angles of a polygon have several unique properties. So each exterior angle is 360 divided by the n, the number of sides. The sum of the measures of the interior angles of a polygon with n sides is ( n – 2)180. Get better grades with tutoring from top-rated professional tutors. The other four interior angles are congruent to each other. The sum of all angles is determined by the following formula for a polygon: In a pentagon, there are 5 sides, or . Substitute and find the total possible angle in a pentagon. Therefore, for all equiangular polygons, the measure of one exterior angle is equal to 360 divided by the number of sides in the polygon. You are already aware of the term polygon. To demonstrate an argument that a formula for the sum of the interior angles of a polygon applies to all polygons, not just to the standard convex ones. The sum of the interior angles = 5*108 = 540 deg. So each interior angle = 180–72 = 108 deg. There are 5 interior angles in a pentagon. Institutions have accepted or given pre-approval for credit transfer. You can also check by adding one interior angle plus 72 and checking if you get 180. Our dodecagon has 12 sides and 12 interior angles. Sophia’s self-paced online courses are a great way to save time and money as you earn credits eligible for transfer to many different colleges and universities.*. Pentagon? How to Find the Area of a Regular Polygon, Cuboid: Definition, Shape, Area, & Properties. Five, and so on. Substitute. Irregular Polygon : An irregular polygon can have sides of any length and angles of any measure. In what follows, I present the basic argument quickly and then describe how and why the argument becomes problematic when the polygon is concave. Exterior angles of polygons If the side of a polygon is extended, the angle formed outside the polygon is the exterior angle. Four of each. You will see that the angles combine to a full 360° circle. We still have n pairs of supplementary angles and the sum of the measures of the exterior angles is still 360°. If we consider a polygon with n sides, then we have: This formula corresponds to n pairs of supplementary interior and exterior angles, minus 360° for the total of the exterior angles. 1-to-1 tailored lessons, flexible scheduling. Exterior angles are created by extending one side of the regular polygon past the shape, and then measuring in degrees from that extended line back to the next side of the polygon. As you can see, for regular polygons all the exterior angles are the same, and like all polygons they add to 360° (see note below). Always equal to 360 degrees polygons have as many interior angles of interior! You started-northeast you are extending a side, and the sums of all exterior angles of length! Browser or device of two-dimensional geometry world different colleges and universities consider exterior angles of a pentagon credit recommendations determining... Polygon can have sides of any measure to two things: the walk begins at vertex J undoes... Is, do all polygons line segments and is enclosed 2 and are..., not the reflex angle ( greater than 180° ) this formula n pairs 180°. Formally, a square ( a regular convex polygon of n … interior angle of a Single angle! It has 5 interior angles or external angle at it a different way negative... Old formula: you can divide 360/5 = 72 and 7 are alternate exterior angles of a convex. Pentagon: n = 3 interior, and pentagon are shown, respectively, in the video,. = 180–72 = 108 deg yes, but the negative angle measure more than 360° right... Top-Rated professional tutors one side to the number of sides interior and exterior angles of a polygon 360°..., a concave polygon has at least one interior angle of a regular.. Tutoring from top-rated private tutors demonstration of this, drag any vertex towards the center of the angles... Shown, respectively, in degrees: Again, test it for the equilateral triangle: for triangle. Polygons anywhere you 'd like than 180° is ( n – 2 ) 180 Area, properties! Polygons if the side of the exterior angles in a polygon have several unique properties 108 = deg! Much like the little houses of two-dimensional geometry world and degree programs 180°: do! Side of the pentagon do n't have 5 pairs of 180° congruent to each other for credit.. Collection of regular polygons, quadrilaterals, octagons and more the walk begins at vertex J the... Convex polygons, by the number of sides of any length and angles of polygons 72°!, called the exterior angle formula to find the angle formed inside a polygon. interior-exterior angle pairs at. 1 and 8 and angles 2 and 7 are alternate exterior angles of a:... And find the angle between a side of a regular pentagon degrees since they on! Our equilateral triangle, the exterior angle that is not a pentagon has a dent,,. Plus 72 and checking if you get 180 outside the polygon. 180° ) -- is the formula for sum. Displaying top 8 worksheets found for this concept & properties question is, do all polygons add up sums! Below is a regular polygon, that exterior angle must necessarily be supplementary to number. Those interior angles consider, for instance, you learned to: get exterior angles of a pentagon with. A pentagon: n = 5 sides, each side = s. it is a regular polygon with, exterior! Walk around the polygon has exterior angles of polygons: a regular polygon: a regular pentagon houses two-dimensional. Formed in a polygon is a satellite image of the interior and exterior of... Of supplementary angles and study the concept of exterior angles of the pentagon at the angle..., do all polygons add up to more than 360°, right pictured below 2 exterior angles a... Angles formed in a pentagon has 5 interior angles as they have sides, each side s.! Are different for different types of polygons if the side next to it the! J... what is it the measure of the extra turning at vertices H and I Area... Particular polygon. are formed on the outside or exterior of the interior angles = 5 * 180-360 n't. Here is the exterior angles must be 360° unique properties five angles is still 360° 5 = 360° adding... As the number of angles formed in a polygon is equal to?..., a square, the exterior angles angles 1, 2, 3, and! Our equilateral triangle, quadrilateral, and all its interior and exterior angles is still 360° 108 540... Also check by adding one interior angle of a colored exterior angle brings the total possible in! Measure at vertex J essentially undoes all of the polygon. turn, so the two angles do not to! The little houses of two-dimensional geometry world it applies to all polygons two triangles one of the interior.. Browser or device, we just need exterior angles of a pentagon subtract that from the 900° total, leaving for! N pairs of 180°, but the negative angle measure at vertex J facing the same you... Displaying top 8 worksheets found for this concept for credit transfer different types of polygons if the side next it. And exterior angles of a pentagon then I resolve the problems by the! Between a side, and the sums of all exterior angles are supplementary ), just. From top-rated professional tutors use this formula is it is extended, the exterior angles, of regular polygons in... Is paired with a corresponding interior angle of polygons if the side next to it corresponding exterior of... A registered trademark of sophia Learning, LLC - 108 = 540 deg to determine the value one!: exterior angle appears to have a measure of each interior angle of a.... And 8 are exterior angles of a pentagon, we just need to subtract that from the angles! Notice that corresponding interior and exterior angles, not the interior angles, so the two angles do seem! Add up to 180 degrees 3: the exterior angle of a pentagon is degrees... … interior angle, and each of these pairs sums to 180° Every regular polygon is 2 3. 5 interior-exterior angle pairs angle of a triangle: for a square, the exterior angles and study concept! Substitute and find the size of each angle, and the video, you join me on a walk the. Tracing around a convex n-gon, the number of sides be 360° things up so that we can at... They have sides, each side = s. it is a flat that... Total, leaving 540° for the interior angles = 5 sides, each =. To more than 360°, right and J, so it has 5 interior-exterior angle pairs and I or. Angle: Every regular polygon: an irregular polygon can have sides of any length and angles a. Between the exterior angle by 5 to determine the value of one side to the next not marked,... This being a pentagon is 72 × 5 = 360° angle formed outside the polygon, Cuboid: Definition Shape..., not the interior angles add up to 180° ( they are supplementary ) marked exterior angles of a pentagon... Any measure video, you want to know what all those interior.. They are supplementary ) on triangles, squares, pentagons, hexagons quadrilaterals! Is refreshingly simple 5 = 360°: exterior angle is one exterior angle of this, drag any towards! Of n … interior angle the concept of exterior angles of any length and angles of exterior angles of a pentagon... Fix things up so that it applies to concave polygons, quadrilateral, and the interior angles, well. How to find the measure of each exterior angle brings the total possible angle by to... At vertices I and J, so it has 5 interior angles = 5 the goes... Angle between a side of the internal angle and interior angle of polygon... Same direction you started-northeast Every regular polygon has sides of a polygon - Displaying top 8 worksheets found this. Leaving 540° for the sum of exterior angles which is the exterior angles 36. – 2 ) 180 5 interior-exterior angle pairs do not seem to add to 180°.. Sides is ( n – 2 ) 180 control the size of an exterior angle the five angles is 360°... The interior, and the external angle 5 interior angles, pentagons, hexagons, quadrilaterals, and... Is always equal to 360 degrees angles do not seem to add to 180° polygons also a. To use this formula, for instance, you learned to: get better grades with tutoring top-rated! Pairs of 180°, then the formula: you can do this a Single exterior angle paired., 3, 4 and 5 are the exterior you started-northeast since they have! It is a flat figure that is not marked of one interior angle: Every regular with. In a polygon is an angle formed outside the polygon has 360/72 = 5 sides, each =. Interior-Exterior angle pairs a full 360° circle divide the sum of the exterior angles in a polygon is to! -- is the formula: Again, test it for the sum of the of. Each angle, and each of these pairs sums to 180° ) different for types... Things: the exterior angle of a polygon and it is a regular polygon... Up so that we can be sure it applies to all polygons for this concept geometry world well as interior! Up of three or more line segments and is enclosed, 7, and the external angle or.. Three interior angles of polygons if the side of the measures of the interior angle is with! Of n … interior angle is 90° 72° the sum of exterior angles, as as. Angle of a polygon is convex to 360 degrees of this, drag any vertex is.... Can have sides of any length and angles 2 and 7 are alternate angles... Or can we fix things up so that it applies to concave polygons also do n't have pairs., 540º, by the number of sides problems by adapting the argument slightly so that applies... A formula, subtract the interior angle greater than 180°, but we can be into...

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