Question

Find the number of sides of a regular polygon whose exterior and interior angles are in the ratio 1 : 3.

• A. 6
• B. 8
• C. 10
• D. 12

Answer 1

The correct option is B 8

Let no. of sides of regular polygon = $n$
Let exterior angle $=x$
And interior angle $=3x$
Exterior angle and interior angle form a linear pair and their sum is 180${}^{\circ }$
$\therefore x+3x={180}^{\circ }$
$4x={180}^{\circ }\Rightarrow x={45}^{\circ }$

Sum of all exterior angles $=(360{)}^{\circ }$
Number of sides x exterior angle = Sum of all exterior angles

$\Rightarrow {45}^{\circ }\times n={360}^{\circ }$
Hence, n = 8.