Question

An exterior angle of a regular polygon measures 30 degrees.

What is the measure of an interior angle?

Answer 1

Measure of Interior Angle = 180 - Measure of Exterior Angle

Measure of Interior Angle = 180 - 30

Measure of Interior Angle = 150 degrees

Answer 2

the sum of the exterior angles of a polygon equal 360 degrees


so if an exterior angle is 30 then the number of sides or angles in the polygon is found by

360/30 = 12

the polygon has 12 sides

next the angle sum of a polygon is

(n - 2)*180 n = the number of sides

substitute 12 into the formula to find the angle sum

once you know that... divide the angle sum by 12 to get the size of 1 interior angle.