Question

The measure of each interior angle of a regular convex polygon is ${156}^{\circ }$. Find the number of sides this polygon has.

• A. 12
• B. 8
• C. 10
• D. 15

Answer 1

The correct option is D 15

Let us assume that the required number of sides be n.

We know that
Sum of all the internal angles of polygon $=180\times (n-2)$
$180\times (n-2)=156\times n\Rightarrow 180n-{360}^{\circ }=156n\Rightarrow 180n-156n=360\Rightarrow 24n=360\Rightarrow n=\frac{360}{24}=15$