Question

Number of sides of a polygon whose exterior and interior angles are in the ratio 1 : 3 is .

• A. 6
• B. 8
• C. 10
• D. 12

Answer 1

The correct option is B 8

Let no. of sides of polygon = $n$
Exterior angle $=x^{\circ }$
Interior angle $=3x^{\circ }$
$x^{\circ }+3x^{\circ }={180}^{\circ }$
($\because \text{sum of exterior angle and interior angle is}{180}^{\circ })$
$4x={180}^{\circ }⟹x={45}^{\circ }$
Sum of all exterior angles $=(360{)}^{\circ }$
$\Rightarrow {45}^{\circ }\times n={360}^{\circ }$
Hence, n = 8.