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m11gmse_0601_FPL2.indd 353 6-1 Solve It! Objectives To find the sum of the measures of the interior angles of a polygon To find the sum of the measures of the exterior angles of a polygon You don’t need to draw all the diagonals from every vertex. Sketch a convex pentagon, hexagon, and heptagon. For each figure, draw all the diagonals you can from one vertex. What conjecture can you make about the relationship between the number of sides of a polygon and the number of triangles that its diagonals form? 6-1 Lesson Quiz 1. What is the sum of the angle measures of a 14-gon? 2. What is the measure of each angle of a regular pentagon? A 3. What is m/C in pentagon ABCDE? E B 105 86 137 C D 4. What is the measure of an exterior angle of a regular pentagon? 1 5. Do you UNDERSTAND? How many sides does a regular polygon have if each exterior angle is 248? How do you know? Answers Solve It! Lesson Quiz Answers may vary. Sample: 1. 2. 3. 4. 5. The number of > formed by the diagonals is 2 less than the number of sides of the polygon. 2/11/09 11:39:51 PM 2160 108 122 72 The sum of the exterior angles of any polygon is 3608, so the number of sides is 360 24 or 15. Prentice Hall Geometry • Solve It/Lesson Quiz on Transparencies Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 37