Question

How do you find the measure of an exterior angle of a regular polygon with 40 sides?

Answer 1

Hint: We are given a regular polygon with 40 sides and we have to find the value of its exterior angle. We know that, for any polygon the sum of the exterior angles is \[{{360}^{\circ }}\]. So, if we divide the total sum of the exterior angles by the number of sides of that polygon, we will get the value of each exterior angle of that particular polygon, in our case, we will divide \[{{360}^{\circ }}\] by \[40\] and the answer that we will get is the value of the exterior angle.

Complete step by step solution:
According to the question given to us, we have a regular polygon which has \[40\] sides. And we are asked to find the value of the exterior angle.
We know the fact that the sum of all exterior angles in any regular polygon is always \[{{360}^{\circ }}\].
In order to find the value of the exterior angle of a polygon, we will have to divide the total sum of the exterior angles by the number of sides of that polygon, that is, \[\dfrac{{{360}^{\circ }}}{n}\] where \[n\] is the number of sides of the polygon.
The given question has the number of sides as 40.
So, the value of the exterior angle is,
\[\dfrac{{{360}^{\circ }}}{40}\]
Dividing \[{{360}^{\circ }}\] by 40, we get the value as,
\[\Rightarrow {{9}^{\circ }}\]

Therefore, the value of the exterior angle of the given regular polygon is \[{{9}^{\circ }}\].

Note: The calculation should be done correctly and the question should be read correctly. There are two types of angles which can be asked, one is exterior angle and the interior angle. Based on what is asked in the question, we will carry out the required.
The sum of the interior angle is calculated according to the formula, \[(n-2)\times {{180}^{\circ }}\], where \[n\] is the number of sides of a polygon.