Section 3 5 Angles of a Polygon many

Section 3 -5 Angles of a Polygon

many angles two endpoint collinear Yes Yes No No No

the interior polygon Yes No a point in of the Yes No

Number of Sides 3 4 5 6 7 8 9 10 n Name of Polygon triangle quadrilateral pentagon hexagon heptagon octagon nonagon decagon n-gon

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

vertices two nonconsecutive

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

1440° 1. What is the interior angle sum of a decagon? _____ (n – 2)180 (10 – 2)180 (8)180 1080° 2. What is the interior angle sum of an octagon? _____ (n – 2)180 (8 – 2)180 (6)180 3. What is the interior angle sum of 22 -gon? ____ 3600° (n – 2)180 (22 – 2)180 (20)180

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

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

Regular Polygon – a polygon that is both equilateral equiangular ______ and ________. 6. What is the measure of one interior angle of 120° a regular hexagon? _____ 7. What is the measure of one interior angle of 108° a regular pentagon? ___________

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

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

11. What polygon has an exterior angle 15 -gon measuring 24°? ___________ 24 n = 360 n = 15 12. What polygon has an interior angle octagon measuring 135°? ___________ (n – 2)180 = 135 n – 360 = – 45 n 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, always is _____ 360°. 14. The sum of the measures of the angles of a sometimes convex polygon is _______ 360°. 15. A segment joining two vertices of a polygon sometimes is ________ a diagonal.

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

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

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