Question

Exterior angles of a regular polygon is one-third of its interior angle. Find number of sides in polygon.

• A. 10
• B. 8
• C. 6
• D. 9

Answer 1

Answer: (B)

8

If we take $n$ as the number of sides of polygon and $E$ be the exterior angle and $I$ be the interior angle.

$\Rightarrow$ $E+I={180}^{\circ }$

According to the given question we get,

$\Rightarrow$ $E=\frac{1}{3}I$

$\Rightarrow$ So, $I=3E$

$\therefore$ $E+3E={180}^{\circ }$

$\Rightarrow$ $E={45}^{\circ }$

$\Rightarrow$ Interior angle $={135}^{\circ }$

$\Rightarrow$ Interior angle $=\frac{(n-2)\times 180}{n}$

$\Rightarrow$ $135n=180n-360$

$\Rightarrow$ $-45=-360$

$\Rightarrow$ $n=8$

$\therefore$ Number of sides in polygon are $8$.