Question

If each interior angle of a regular polygon is 150°, then it has _____ sides.

• A. 12
• B. 11
• C. 10
• D. 9

Answer 1

The correct option is A

12

It is given that the polygon is regular. So all the sides and angles of the polygon are equal.

$\because$ exterior angle = 180° - interior angle

= 180° - 150°

= 30°

$\because$ Sum of exterior angles of any polygon = 360${}^{\circ }$

$\Rightarrow$ n $\times$ exterior angle = 360${}^{\circ }$ (where, n= Number of sides)

$\Rightarrow$ n =$\frac{360°}{\text{exterior angle}}$

= $\frac{360°}{30°}$

= 12

$\therefore$ Number of sides = 12.