Question

Find the measures of each exterior angle of a regular decagon.

Answer 1

Hint: Here, we need to find the measure of each exterior angle of a regular decagon. Now, a regular decagon has 10 sides and 10 angles and all these angles and sides are equal. The formula used to find the interior angle and exterior angle of a regular decagon is
$\to$Interior angle$=180-$exterior angle
$\to$Exterior angle $={\displaystyle \frac{360}{n}}$

Complete step-by-step solution:
In this question, we are supposed to find the measure of each exterior angle of a regular decagon.
First of all, what is the shape of the shape of a regular decagon?
A regular decagon has the following shape.

Decagon has ten sides and ten angles.
All these sides and angles are equal to each other.
As a decagon has 10 sides, the formula for exterior angle is given by
$\to$Exterior angle $={\displaystyle \frac{360}{n}}={\displaystyle \frac{360}{10}}={36}^{\circ }$
Therefore, the measure of each exterior angle of a regular decagon is ${36}^{\circ }$.

Note: The difference between regular decagon and irregular decagon is that regular decagon has all the sides and angles equal and an irregular decagon has irregular sides and angles that means different sides and different angles.
Now, the formula to find the interior angle of a regular decagon is given by
$\to$Interior angle$=180-$exterior angle.
Now, as we found that each exterior angle of a regular decagon is 36, its interior angle will be
$\to$Interior angle$=180-36={144}^{\circ }$
Hence, a regular decagon has each exterior angle ${36}^{\circ }$ and each interior angle as ${144}^{\circ }$.