Question

The ratio of the measure of an exterior angle of a regular $7:2$ nonagon to the measure of one of its interior angles is:

• A. $7:2$
• B. $2:7$
• C. $4:3$
• D. $3:4$

Answer 1

The correct option is B $2:7$

Let $7a$ be the interior angle

and $2a$ be the exterior angle

Therefore, $7a+2a={180}^0$

$\Rightarrow 9a={180}^0$

$\Rightarrow a={20}^0$

So, $2a=2\times 20$

$={40}^0$

and $7a=7\times 20$

$={140}^0$

For a regular polygon of $n$ sides, each exterior angle has a measure of $\frac{360}{n}$ degrees.

The measure of each interior angle is ${140}^0$.

Since the exterior angle of each angle has measure ${40}^0$, then the number of sides $n$.

$=\frac{360}{n}$

$=9$ sides.