My Maths and I: WAEC Mathematics Question 2015 ( Essay Question Three 3a )

The ratio of the interior angle to the exterior angle of a regular polygon is 5:2.

Find the number of sides of the polygon.

Solution

Given ratio of interior angle to exterior angle as 5:2, we have;

But the interior angle of a regular polygon is given as $\frac{(n-2)180}{n}$ and the exterior angle as $\frac{360}{n}$

Hence, $\frac{\frac{\frac{(n-2)180}{n}}{360}}{n}=\frac{5}{2}$

Simplifying, we have

$\frac{(n-2)180}{n}\div \frac{360}{n}= \frac{5}{2}$

changing the division sign to multiplication sign, we have

$\frac{(n-2)180}{n}\times \frac{n}{360}= \frac{5}{2}$

$\therefore \frac{(n-2)}{2}= \frac{5}{2}$

2(n-2) = 5 x 2

2n - 4 = 10

2n = 10 + 4

2n = 14

Making n the subject of the formular in the equation we have to divide both side by 2

$\frac{2n}{2}= \frac{14}{2}$

n = 7

ANSWERED

$\therefore$ The number (n) of sides of the polygon is 7

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