Question

Fine the measure of the angle formed by the radius and the side of a regular dodecagon.

A.15
B.30
C.60
D.75

Answer 1

Option D.75°

Explanation:

we know that

The sum of the interior angles of a regular dodecagon is equal to

`S=(n-2)*180`

where

n is the number of sides

In this problem

n=12 sides

substitute

`S=(12-2)*180`

`S=1,800\°`

Find the measure of each interior angle

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

`1,800\°/12=150\°`

The measure of the angle formed by the radius and the side of a regular dodecagon is half the measure of the interior angle

therefore

`150\°/2=75\°`