Question

Find the measure of exterior angle of a regular polygon of 9 sides
A. ${40^ \circ }$
B. ${60^ \circ }$
C. ${50^ \circ }$
D. ${30^ \circ }$

Answer 1

Hint: In the above question, we know that the regular polygon of 9 sides is enclosed figures which have 9 sides, which are equal to each other. Now, we also know that the exterior angle is the angle between the side of the polygon and an extended adjacent side of the polygon. Now, to find the measure of the exterior angle of a regular polygon we will use a formula $\dfrac{{{{360}^ \circ }}}{n}$ , where $n$ is the number of sides of the polygon.

Formula used: We use the formula of the measure of exterior angle of a polygon with side $n$, that is $\dfrac{{{{360}^ \circ }}}{n}$

Complete step-by-step solution:
From the above question we are given a regular polygon of 9 sides.
Now, to find the measure of the exterior angle of the regular polygon, we will use the formula $\dfrac{{{{360}^ \circ }}}{n}$ , where $n$ is the number of sides of the polygon.
Now, we have $n$ which is equal to 9.
Substituting the value of $n$ in the given formula,
$
   \Rightarrow \dfrac{{{{360}^ \circ }}}{n} \\
   \Rightarrow \dfrac{{{{360}^ \circ }}}{9} = {40^ \circ } \\
   \Rightarrow {40^ \circ } \\
 $
Hence, the exterior angle of a regular polygon with 9 sides is ${40^ \circ }$ .

Hence, the correct option is A.

Note: In these types of questions, we need to see that there is a difference between a regular polygon and a simple polygon. A regular polygon has all the side and all the interior angles equal whereas in a simple polygon, the sides and interior angles are different. Now, there is a formula to find the exterior angle of the regular polygon. Now by substituting the value of the sides in the formula will lead us to a correct answer for the problem.