Find the measure of an interior angle and an exterior angle of each regular polygon. 16-gon

Answer 1

To find the measure of an interior angle of a regular polygon, we use the formula:

Interior angle = (n-2) * 180 / n

where n is the number of sides of the polygon.

For a 16-gon:

Interior angle = (16-2) * 180 / 16
Interior angle = 14 * 180 / 16
Interior angle = 2520 / 16
Interior angle = 157.5 degrees

To find the measure of an exterior angle of a regular polygon, we use the formula:

Exterior angle = 360 / n

For a 16-gon:

Exterior angle = 360 / 16
Exterior angle = 22.5 degrees

Therefore, the measure of an interior angle of a 16-gon is 157.5 degrees and the measure of an exterior angle is 22.5 degrees.