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Transcript
Angles and Polygons Course: Geometry Topic: Angles and Polygons Objective: Find the sum of interior angles of polygons. Find measure of exterior angles of polygons. Body: Interior Angle Sum Theorem If a convex polygon has n sides and S is the sum of the measure of its interior angles, Then S = 180(n-2) Example: Find the sum of the measures of the interior angles of a polygon with 32 sides. In a 32-gon n = 32 n being identified as number of sides S = 180(32-2) plug into formula S = 180(30) simplify S = 5400 Example: The measure of an interior angle of a regular polygon is 140 find the number of sides in the polygon. Use formula S = 180(n-2) S = 140n If one angle is 140, then sum is 140 times the number of sides. 140n = 180(n-2) Plug into formula 140n = 180n-360 Simplify 360 = 40n n=9 Exterior Angle Sum Theorem If a polygon is convex, then the sum of the measure of the exterior angles, one at each vertex, is 360. Example Find the measure of an exterior angle and on interior angle of a convex regular octagon. How many sides does an octagon have? 8 The sum of the measures of the interior angles S = 180(n-2) use n=8 S = 180 (8-2) = 1080 Divide 1080 by 8 to get the measure of an interior angle 1080/8=135 To find the measure of an exterior angle, one exterior angle at each angle makes a total of 8 angle. All those angles should add up to 360, so. 8n = 360 n = 45