Question

How many sides does a regular n-gon have if one interior angle measures 150°? Show all work!

Answer 1

A regular n-gon with one interior angle of 150° has 12 sides.

Explanation:

The formula for the measure of each interior angle of a regular n-gon is:

• 180(n-2)/n

where:

• n is the number of sides

We are given that one interior angle measures 150°, so we can set up the equation:

• 180(n-2)/n = 150

Multiplying both sides by n, we get:

• 180(n-2) = 150n

Distributing, we get:

• 180n - 360 = 150n

Subtracting 150n from both sides, we get:

• 30n - 360 = 0

Adding 360 to both sides, we get:

• 30n = 360

Dividing both sides by 30, we get:

• n = 12

Therefore, a regular n-gon with one interior angle of 150° has 12 sides.