Question 42

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waecmaths question: 

An interior angle of a regular polygon is 5 times each exterior angle. How many sides has the polygon

Option A: 

15

Option B: 

12

Option C: 

9

Option D: 

6

waecmaths solution: 

$\begin{align}  & \text{Let the exterior angle be }x \\ & \text{The interior angle will be }5x \\ & \therefore 5x+x={{180}^{\circ }} \\ & x={{30}^{\circ }} \\ & \text{Each exterior angle has }{{30}^{\circ }} \\ & \text{The sum of all exterior angle }={{360}^{\circ }} \\ & {{30}^{\circ }}n={{360}^{\circ }} \\ & n=\frac{{{360}^{\circ }}}{{{30}^{\circ }}}=12 \\\end{align}$

maths year: