The ratio of the exterior angle to the interior angle of a regular polygon is 1:11. How many sides has the polygon?

  • A 30
  • B 24
  • C 18
  • D 12
waec 2016mathematics

The correct answer is B. 24

Let a represent an interior angle; e represent an exterior angle. A section of the polygon is down in the diagram.

\(\frac{e}{a}\) = \(\frac{l}{11}\) given

a = 11e

a + e = 180o(angles on a straight line)

11e + e = 180o

12e = 180o

e = \(\frac{180^o}{12}\)

= 15o

Hence, number of sides

= \(\frac{360^o}{\tect{size of one exterior angle}\)

= \(\frac{360^o}{14^o}\)

= 24

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