Question

If the sum of exterior angles of a polygon is one-ninth the sum of its interior angles, then the polygon has ___ sides.

• A. 20
• B. 18
• C. 180
• D. 182

Answer 1

The correct option is A

20

Let the number of sides = n

Sum of exterior angles of a polygon = ${360}^{\circ }$

Sum of interior angles of n sided polygon $=(2n-4)\times {90}^{\circ }$

Given, sum of exterior angles of a polygon is one-ninth the sum of its interior angles

$\Rightarrow 360=\frac{1}{9}\left[\right(2n-4)\times {90}^{\circ }]$

$\Rightarrow$ 360 = (2n - 4)$\times 10$

$\Rightarrow$36 = 2n - 4

$\Rightarrow$2n = 40

$\Rightarrow$n = 20

$\therefore$ The given polygon has 20 sides.