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 = ${360}^{\circ }$

Sum of interior angles $=(n-2)\times {180}^{\circ }$

Given,

$360=\frac{1}{9}\left[\right(n-2)\times {180}^{\circ }]$

360 = (n - 2) 20

18 = n - 2

n = 20

Hence (A)