Question

Each interior angle of a regular polygon is $150°$ . How many sides does it have ?

• A. $10$
• B. $11$
• C. $12$
• D. $8$

Answer 1

The correct option is C

$12$

As we know that the measures of each interior angles of a polygon having $n$ sides is$=\frac{(n-2)\times 180}{n}$

Now the measure of given interior angle is $=150°$

$$\begin{gathered} 150°=\frac{(n-2)\times 180}{n} \\ 150n=180n-360 \\ n=\frac{360}{30}=12 \end{gathered}$$
Thus, the number of sides of a regular polygon is $12$.

Hence, option C is the correct option.