Question

What is the sum of the interior angle measures of a regular decagon? ° What is the measure of each interior angle of a regular decagon? °

Answer 1

1. 1440

2. 144

Explanation:

EDG 2020

Answer 2

Part a) The sum of the interior angle measures of a regular decagon is
`1,440\°`

Part b) The measure of each interior angle of a regular decagon is
`144\°`

Explanation:

Part a)

we know that

The sum of the interior angles of a polygon is equal to

`S=(n-2)180\°`

where

n is the number of sides of a polygon

In this problem

`n=10` ----> regular decagon

substitute

`S=(10-2)180\°=1,440\°`

Part b) What is the measure of each interior angle of a regular decagon?

If the figure is a regular polygon, then all interior angles are equal

so

Divide the sum of the interior angles by the number of sides

`1,440\°/10=144\°`