Question

The interior angles of a regular polygon measure ${150}^o$ each. The number of diagonals of the polygon is

• A. $35$
• B. $44$
• C. $54$
• D. $78$

Answer 1

The correct option is C $54$

Measure of each interior angle of a regular polygon is ${150}^o$

$\Rightarrow \frac{(n-2)\times {180}^o}{n}={150}^o$

$\Rightarrow 180n-150n=360$

$\Rightarrow 30n=360$

$\Rightarrow n=12$

Thus the given regular polygon is a $12$ sided regular polygon.

We know that, number of diagonals in a regular polygon is $\frac{n(n-3)}{2}$

So, number of diagonals $=\frac{12(12–3)}{2}=\frac{9\times 12}{2}=\frac{108}{2}=54$

Hence the number of diagonals of the given polygon is $54$.