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LESSON 11.1 NAME _________________________________________________________ DATE ____________ Practice with Examples For use with pages 661–668 GOAL Find the measures of interior and exterior angles of polygons VOCABULARY Theorem 11.1 Polygon Interior Angles Theorem The sum of the measures of the interior angles of a convex n-gon is n 2 180. Chapter 11 Corollary to Theorem 11.1 The measure of each interior angle of a regular n-gon is 1 n n 2 180, or n 2 180 . n Theorem 11.2 Polygon Exterior Angles Theorem The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360. Corollary to Theorem 11.2 The measure of each exterior angle of a regular n-gon is 1 n EXAMPLE 1 360, or 360 . n Finding Measures of Interior Angles of Polygons Find the value of x. 115 96 SOLUTION The sum of the measure of the interior angles of any pentagon is 5 2 180 3 180 540. 64 x Add the measures of the interior angles of the pentagon. 64 115 96 90 x 540 365 x 540 x 175 202 Geometry Practice Workbook with Examples The sum is 540. Simplify. Subtract 365 from each side. Copyright © McDougal Littell Inc. All rights reserved. LESSON 11.1 CONTINUED NAME _________________________________________________________ DATE ____________ Practice with Examples For use with pages 661–668 Exercises for Example 1 In Exercises 1–3, find the value of x. 1. 2. 120 3. x 125 125 x 135 112 160 130 4x 115 3x 125 135 EXAMPLE 2 82 135 Finding the Number of Sides of a Polygon The measure of each interior angle of a regular polygon is 144. How many sides does the polygon have? SOLUTION 1 n n 2 180 144 n 2 180 144n 180n 360 144n n 10 Corollary to Theorem 11.1 Multiply each side by n. Distributive property Solve for n. Exercise for Example 2 4. The measure of each interior angle of a regular n-gon is 156. Find the value of n. Copyright © McDougal Littell Inc. All rights reserved. Geometry Practice Workbook with Examples 203 Chapter 11 135 LESSON 11.1 CONTINUED EXAMPLE 3 NAME _________________________________________________________ DATE ____________ Practice with Examples For use with pages 661–668 Finding the Measure of an Exterior Angle Find the value of x in each diagram. a. b. Chapter 11 2x 70 x 80 x 60 SOLUTION a. x 90 2x 70 80 60 360 3x 60 x 20 b. x 1 5 360 Theorem 11.2 Combine like terms. Divide each side by 3. Use n 5 in the Corollary to Theorem 11.2. x 72 Simplify. Exercises for Example 3 Find the value of x. 5. 6. 3x 76 52 x 204 Geometry Practice Workbook with Examples Copyright © McDougal Littell Inc. All rights reserved.