Section 3-5 Angles of a Polygon

many two endpoint collinear Yes No angles

a the polygon Yes No point in interior ofthe

Number of SidesName of Polygon n triangle hexagon octagon decagon n-gon pentagon quadrilateral heptagon nonagon

consecutive vertices C D E B C D A E D E A B A B C D C B

two nonconsecutive vertices

Theorem 3-13 The sum of the measures of the angles of a convex polygon with n sides is _____________________. (n – 2) 180

1. What is the interior angle sum of a decagon? _____ 2. What is the interior angle sum of an octagon? _____ 3. What is the interior angle sum of 22-gon? ________ (n – 2)180 (10 – 2)180 (8) ° (n – 2)180 (8 – 2)180 (6) ° (n – 2)180 (22 – 2)180 (20) °

Theorem 3-14 The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is __________. 360°

4. What is the exterior angle sum of a pentagon? _______________________ 5. What is the exterior angle sum of a decagon? _______________________ 360°

Regular Polygon – a polygon that is both ____________ and ________________. 6. What is the measure of one interior angle of a regular hexagon?__________ 7. What is the measure of one interior angle of a regular pentagon?_____________________ equilateralequiangular 120° 108°

8. What is the measure of one interior angle of a regular decagon? ____________________ 144°

9. What is the measure of one exterior angle of a regular hexagon? _______________________ 10. What is the measure of one exterior angle of a regular octagon? _____________________ 60° 45°

11. What polygon has an exterior angle measuring 24°?______________________ 12. What polygon has an interior angle measuring 135°? ______________________ 15-gon 24n = 360 n = 15 octagon (n – 2)180 = 135n – 360 = –45n 8 = n

Complete with always, sometimes, or never. 13. The sum of the measures of the exterior angles of any polygon, one angle at each vertex, is __________ 360°. 14. The sum of the measures of the angles of a convex polygon is ______________ 360°. 15. A segment joining two vertices of a polygon is ________________ a diagonal. always sometimes

16. The sum of the measures of the exterior angles of a polygon _____________ depends on the number of sides of the polygon. 17. A regular polygon is __________ equilateral. 18. An equiangular polygon is _________ regular. never always sometimes

19. Three of the angles of a quadrilateral have measures 90, 60, and 115. The fourth angle has measure________. 95° x = 360 (4 – 2) 180 = 360

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