Question

Two times the interior angle of a regular polygon is equal to seven times is exterior angle. Find the interior angle of the polygon and the number of sides in it.

• A. ${130}^{\circ }$ and n $=$ 9
• B. ${140}^{\circ }$ and n $=$ 9
• C. ${160}^{\circ }$ and n $=$ 9
• D. ${170}^{\circ }$ and n $=$ 9

Answer 1

The correct option is B ${140}^{\circ }$ and n $=$ 9

Two times the interior angle of a regular polygon is equal to seven times is exterior angle.
Each Interior angle of a polygon = $\frac{{180}^o(n-2)}{n}$
Each Exterior angle of a polygon = $\frac{{360}^o}{n}$
Now,
$2\times \frac{{180}^o(n-2)}{n}=7\times \frac{{360}^o}{n}$
$=>n-2=7$
$=>n=9$
Number of sides of polygon is 9.
Each Interior angle of a polygon = $\frac{{180}^o(n-2)}{n}=\frac{{180}^o(9-2)}{9}={140}^o$