What is the measure of each of the interior angles of these regular polygons?

a) pentagon
b) octagon
c) dodecagon

How would I figure this out?

add up the exterior angles between the extension of one side and the next side.

They must add up to 360 because they go all the way around.
Then the interior angle is the supplement.

For example for a regular pentagon
exterior between side extension and side = 360/5 = 72
so each interior angle is
180 - 72 = 108

To find the measure of each interior angle of a regular polygon, you can use the formula:

Interior Angle = (n-2) * 180° / n

In this formula, "n" represents the number of sides of the polygon.

a) For a pentagon (5 sides), you can substitute the value of "n" into the formula:

Interior Angle = (5-2) * 180° / 5
= 3 * 180° / 5
= 540° / 5
= 108°

Therefore, each interior angle of a pentagon measures 108 degrees.

b) For an octagon (8 sides):

Interior Angle = (8-2) * 180° / 8
= 6 * 180° / 8
= 1080° / 8
= 135°

Therefore, each interior angle of an octagon measures 135 degrees.

c) For a dodecagon (12 sides):

Interior Angle = (12-2) * 180° / 12
= 10 * 180° / 12
= 1800° / 12
= 150°

Therefore, each interior angle of a dodecagon measures 150 degrees.

By substituting the number of sides into the formula (n-2) * 180° / n, you can find the measure of each interior angle of any regular polygon.