An interior angle of a regular polygon is 5 times each exterior angle. How many
MATHEMATICS
WAEC 2013
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
Correct Answer: B. 12
Explanation
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
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