20. Find the measure of each interior angle AND each exterior angles of the following regular polygons. Show your work. a. Pentagon b. 16-gon c. Dodecagon
Accepted Solution
A:
a. Pentagon
Interior angle:
5 sides => form 5 triangles => central angle: 360 / 5 = 72°
interior angle = 2x
angles in every triangle: x => x + x + 72° = 180°
=> 2x = 180° - 72° = 108°
Answer 108°
Exterior angles = 360° / number of sides = 360° / 5 = 72°
Answer: 72°
b. 16 - gon
Interior angles: 2x
number of triangles = 16
central angle = 360 / 16 = 22.5°
interior angle 2x, where 180° - 22.5° + x + x => 2x = 180° - 22.5° = 157.5°