Question

What is the measure of one exterior angle of a regular decagon?

Answer 1

Answer:

Exterior angle of decagon = 36°

Step-by-step explanation:

Given problem is about finding measure of one exterior angle of a regular decagon

⇒ number of the sides in decagon = 10

⇒ in a regular polygon with number of sides "n"  

measure of each interior angle = (n−2)×180°/ n  

⇒each interior angle in decagon =[(10-2)× 180°]/ 10

                                                       = [8×180]/ 10

                                                       = 8 × 18 = 144°

⇒ interior angle in decagon = 144°

⇒ we know that sum of interior and exterior angles =180°

⇒  interior angle + exterior angle = 180°

⇒  exterior angle = 180° - interior angle    

                             = 180° - 144° = 36°  

⇒exterior angle of decagon = 36°

Answer 2

Given:

A regular decagon.

To find:

The measure of one exterior angle of a regular decagon.

Solution:

The measure of one exterior angle of a regular decagon is 36°.

To answer this question, we will follow the following steps:

As we know that a regular decagon has 10 sides and hence, 10 angles.

Also,

We should know that the formula for finding the measure of one exterior angle of a regular polygon is given by:

$\frac{360°}{n}$

where n = number of angles of a regular polygon.

Now,

We have a regular decagon having 10 angles

So,

One of the exterior angles of a regular decagon is

$= \frac{360°}{10}$

$= 36°$

Hence, the measure of one exterior angle of a regular decagon is 36°.