Question

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

Answer 1

Answer:

Option D.75°

Step-by-step 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

$150\°/2=75\°$