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?

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

where

n is the number of sides of regular polygon

In this problem a regular dodecagon has n=12 sides

substitute

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

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

solve for x

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.