Question

What is the measure of the sum of all angles in a regular dodecagon (12 sides)? What is the measure of one of its interiors angles and one of its exterior angles?

Answer 1

Answer:

Part a) The measure of the sum  of all angles in a regular dodecagon is equal to 1,800 degrees

Part b) The measure of one of its interiors angles is 150 degrees

Part c) The measure of one of its exterior angles is 30 degrees

Step-by-step explanation:

Part a) What is the measure of the sum of all angles in a regular dodecagon (12 sides)

we know that

The formula to calculate the sum of the interior angles in a regular polygon is equal to

$S=(n-2)180^o$

where

n is the number of sides of regular polygon

In this problem a regular dodecagon has n=12 sides

substitute

$S=(12-2)180^o$

$S=(10)180^o$

$S=1,800^o$

Part b) What is the measure of one of its interiors angles?

To find out the measure of one of its interior angles, divide the sum of all angles by the number of sides

$1,800^o/12=150^o$

Part c) What is the measure of one of its exterior angles?

we know that

The sum of one interior angle and its corresponding exterior angle must be equal to 180 degrees

Let

x ---> the measure of one exterior angle

$150^o+x=180^o$

solve for x

$x=180^o-150^o$

$x=30^o$