Question

A regular polygon has an interior angle of 171 degrees. Show your work. (3 points for work, 3 points

Answer 1

Answer:

a) 40 sides

b) 6840

c) 9 gegrees

Step-by-step explanation:

interior angle= (n-2)180

n

$(n - 2)180 \div n = 171 \\ 180n - 360 = 171n \\ 180n - 171n = 360 \\ 9n = 360 \\ n = 360 \div 9 = 40$

so total number of sides is 40

b) Sum of interior angles= (n-2)×180

(40-2)×180

38×180

6840

c) Exterior angle = 360 ÷ n

360÷40 =9 degree