The ratio of the exterior angle to the interior... - WAEC Mathematics 2016 Question

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 = 180^o(angles on a straight line)

11e + e = 180^o

12e = 180^o

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

= 15^o

Hence, number of sides

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

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

= 24