Question

The measure of each interior angle of a regular polygon is 150 degrees

True or false: the polygon has 12 sides.

Answer 1

True

Explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 12

sum = 180° × 10 = 1800°, hence

interior angle =
`(1800)/(12)` = 150° → True

Answer 2

True

Explanation:

The formula sum of interior angles = (n-2) * 180

n = the number of sides

We plug in the numbers in the formula

We add times 12 on the left side because you are supposed to put the total sum of the interior angles and 150 is just 1 of the angle

150*12 = (12-2) *180

1800 = 10 *180

1800 = 1800