Question

Find the number of sides of a polygon whose exterior and interior angles are in the ratio 1 : .5

• A. 10
• B. 15
• C. 12
• D. 14

Answer 1

The correct option is C

12

Let no. of sides of polygon = n
Exterior angle $=x^{\circ }$
Interior angle $=5x^{\circ }$
$x={30}^{\circ }(\because {\text{sum of exterior angle + inteior angle is 180}}^{\circ })$
Sum of all exterior angles $=(360{)}^{\circ }$
$\Rightarrow {30}^{\circ }\times n={360}^{\circ }$
Hence, n = 12.