Question

The sum of exterior angles of a polygon is one-third of the sum of interior angles. Find the number of sides in the polygon.

• A. 6
• B. 5
• C. 8
• D. 10

Answer 1

The correct option is C

8

Sum of exterior angles of a polygon is ${360}^o$.

Let the sum of interior angles be $x$.

$\Rightarrow \frac{1}{3}\times x={360}^o$

$\Rightarrow x={360}^o\times 3$

= ${1080}^o$

$\because$ Sum of interior angles = (2n-4) $\times$ 90${}^o$, where n is number of sides in polygon

$\Rightarrow$ (2n-4) $\times$ 90${}^o$ = 1080${}^o$

$\Rightarrow$ (2n-4) $\times$ 90${}^o$ = (90 $\times$ 12)${}^o$

$\Rightarrow$ (2n-4) = 12

$\Rightarrow$ n = 8

$\therefore$ Number of sides in the given polygon is 8.