THEOREM 8.1. Polygon Interior Angles Theorem. interior angles of a convex polygon with n sides is (n 2)p180.


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1 Page of 7 8. ngles in Polygons Goal Find the measures of interior and exterior angles of polygons. The definitions for interior angles and exterior angles can be extended to include angles formed in any polygon. In the diagrams shown below, interior angles are red, and exterior angles are blue. Key Words interior angle p. 8 exterior angle p. 8 interior angles exterior angles ctivity 8. suggests the Polygon Interior ngles Theorem shown below. THORM 8. Polygon Interior ngles Theorem Words The sum of the measures of the interior angles of a convex polygon with n sides is (n )p80. Symbols ma ma... man (n )p80 6 n 6 XMPL Use the Polygon Interior ngles Theorem Find the sum of the measures of the interior angles of a convex heptagon. heptagon has 7 sides. Use the Polygon Interior ngles Theorem and substitute 7 for n. (n )p80 (7 )p80 Substitute 7 for n. p Simplify. Multiply. NSWR The sum of the measures of the interior angles of a convex heptagon is ngles in Polygons 7
2 Page of 7 XMPL Find the measure of a in the diagram. Find the Measure of an Interior ngle The polygon has 6 sides, so the sum of the measures of the interior angles is: (n )p80 (6 )p80 p F Student Help SKILLS RVIW To review solving an equation, see p. 67. dd the measures of the interior angles and set the sum equal to ma 70 The sum is ma 70 Simplify. ma Subtract 607. NSWR The measure of a is. XMPL Find the measure of an interior angle of a regular octagon. The sum of the measures of the interior angles of any octagon is: (n )p80 (8 )p80 6p ecause the octagon is regular, each angle has the same measure. So, divide 080 by 8 to find the measure of one interior angle Interior ngles of a Regular Polygon NSWR The measure of an interior angle of a regular octagon is. Find Measures of Interior ngles In xercises, find the measure of ag.. F G. H. H J J G F 0 0 G 8 H L M K K. Find the measure of an interior angle of a regular polygon with twelve sides. 8 hapter 8 Polygons and rea
3 Page of 7 xterior ngles The diagrams below show that the sum of the measures of the exterior angles of the convex polygon is 60. Visualize It! circle contains two straight angles. So, there are 80 80, or 60, in a circle or 60 Shade one exterior ut out the rrange the exterior angle at each vertex. exterior angles. angles to form The sum of the measures of the exterior angles of a convex polygon does not depend on the number of sides that the polygon has. THORM 8. Polygon xterior ngles Theorem Words The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 60. Symbols ma ma... man 60 n XMPL Find the value of x. Find the Measure of an xterior ngle Using the Polygon xterior ngles Theorem, set the sum of the measures of the exterior angles equal to Polygon xterior ngles Theorem 80 x 60 ombine like terms. x 80 NSWR The value of x is Subtract 80 from each side. x 60 ivide each side by. 8. ngles in Polygons 9
4 Page of 7 Find xterior ngle Measures Find the value of x xercises Guided Practice Vocabulary heck. Name an interior angle and an exterior angle of polygon shown at the right. G Skill heck. Write the formula that is used to find the sum of the measures of the interior angles of any convex polygon with n sides. F H. Use your answer from xercise to find the sum of the measures of the interior angles of a convex polygon with 9 sides. Write an equation to find the measure of a. o not solve the equation hapter 8 Polygons and rea
5 Page of 7 Practice and pplications xtra Practice See p Sum of Interior ngle Measures Find the sum of the measures of the interior angles of the convex polygon Polygons with n Sides Find the sum of the measures of the interior angles of the convex polygon with n sides.. n 0. n. n 0. n 0. n 6. n 00 Interior ngle Measures Find the measure of a F F IStudent Help I L S S Z O N. O M HOMWORK HLP xtra help with problem solving in xs. is at classzone.com Interior ngles of Regular Polygons Find the measure of an interior angle of the regular polygon.... Using lgebra Find the value of x. Homework Help xample : xs. 8 6 xample : xs. 7 0 xample : xs. xample : xs., ngles in Polygons
6 Page 6 of 7 Sports aseball home plate for a baseball field is a pentagon as shown. 6. Is the polygon regular? xplain why or why not. 7. What is the sum of the interior angles? 8. Find the measures of a and a. SLL Home plate is used to find the placement of the foul lines on the playing field. Visualize It! ut a strip of lined paper and tie it into an overhand knot as shown. Gently flatten the knot to form a pentagon. The pentagon should be regular. 9. Find the measure of an interior angle of a regular pentagon. 0. Measure the interior angles of your knot with a protractor. Use your answer to xercise 9 to determine whether your pentagon is regular. Logical Reasoning Select the word that makes the statement true.. The sum of the measures of the exterior angles of a convex polygon, one at each vertex, is (always, sometimes, never) 60.. The sum of the measures of the interior angles of a convex octagon is (always, sometimes, never) 0.. The measures of the exterior angles of a convex polygon are (always, sometimes, never) equal.. Outdoor Furniture You are constructing a regular hexagonal wooden bench like the one shown. On the bench, a ca. Find the measures of a and a so that you know what angle to use to cut the pieces of wood. hallenge Find the number of sides of the regular polygon with the given exterior angle measure hapter 8 Polygons and rea
7 Page 7 of 7 Standardized Test Practice Multiple hoice In xercises 9 and 0, use the diagram below. 9. What is the value of x? What is the measure of ap? P P 0 0 U R S 0 T F 9 G 78 H 6 J Mixed Review Using a entroid is the centroid of T. Find and. (Lesson.6). 6.. lgebra Skills bsolute Value valuate. (Skills Review, p. 66) Quiz ecide whether the polygon is regular. xplain your answer. (Lesson 8.)... Find the measure of a. (Lesson 8.) ngles in Polygons
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