Question

In a regular polygon if the ratio of inner and outer angle is 7:2, then find the number of sides in the polygon.

• A. 7
• B. 8
• C. 9
• D. 10

Answer 1

The correct option is C

9

Given that the polygon is regular and the ratio of inner and outer angle = 7:2

Let the inner angle = 7$x$ and outer angle = 2$x$ and the number of sides in the polygon be 'n'.

$\because$ The polygon is regular, all the inner angles are equal and all the outer angles are equal.

$\therefore$ Sum of interior angles = 7$x$ $\times$ n and Sum of outer angles = 2$x$ $\times$ n

$\because$ Sum of outer angles in a polygon = 360${}^{\circ }$

$\Rightarrow$ 2$x$ $\times$ n = 360${}^{\circ }$

$\Rightarrow$ n$x$ = 180${}^{\circ }$--------(1)

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

$\Rightarrow$ 7$x$ $\times$ n = (n-2) $\times$ 180${}^{\circ }$

$\Rightarrow$ 7 $\times$ 180 = (n-2) $\times$ 180${}^{\circ }$ $(\because \text{n}x={180}^{\circ }$)

$\Rightarrow$ 7 = n-2

$\Rightarrow$ n = 9

$\therefore$ Number of sides in the given polygon is 9.