Question

The sum of the interior angles and the sum of exterior angles of a polygon are in the ratio $9:2$. Find the number of sides in the polygon.

Answer 1

The sum of the internal angles of a polygon is = ${180}^o(n-2)$

Sum of exterior angle of a polygon is = ${360}^o$

The sum of the interior angles and the sum of exterior angles of a polygon are in the ratio 9:2.

Then, $\frac{{180}^o(n-2)}{{360}^o}=\frac{9}{2}$

$=>\frac{(n-2)}{2}=\frac{9}{2}$

$=>n-2=9$

$=>n=11$