# How is an exterior angle of a polygon formed?

180 - interior angle = exterior angle

### What is exterior of an angle?

The interior angle of a polygon is the angle formed by two adjacent sides of a polygon where the angle lies inside the area formed by the polygon. The exterior angle is that formed by one of these sides and the line formed by extending the other side. Consequently, External angle = 180 deg - Internal angle. Because they form supplementary angles, it does not matter which of the two sides you extend.

### How many sides does an equiangular polygon have if the measure of an angle of the polygon exceeds four times the measure of one of it's exterior angles by 30?

Interior angle + Exterior angle = 180 So Interior angle = 180 - Exterior angle Interior angle = 4*Exterior angle + 30 Substitute for Interior angle: 180 - Exterior angle = 4*Exterior angle + 30 Collect like terms: 150 = 5*Exterior angle Divide by 5: Exterior angle = 30 deg Therefore number of sides = 360/30 = 12