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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
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Correct Answer: Option B
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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