An interior angle of a regular polygon is 5 times each exterior angle. How many sides has the polygon?
A
15
B
12
C
9
D
6
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
Let the interior angle = xo
interior angle = 5xo (sum of int. angle ann exterior)
(angles = angle or straight line)
6x = 180
x = \(\frac{180}{6}\)
x = 30o
no. of sides = \(\frac{\text{sum of exterior angles}}{\text{exterior angle}}\)
= \(\frac{360}{30}\) = 12
Source: Myschool Past Questions Archive (Record #36898)