What is the measure of the supplementary angle of an interior angle of a regular polygon?

Solution:

Two angles are said to be supplementary angles if they add up to 180 degrees. The supplementary angle to any angle is 180 degrees minus that angle.

For a regular polygon, all interior angles are equal so we can calculate the supplementary angle to any one of the interior angles.

The sum of all the interior angles of a regular polygon = (n - 2) × 180º, where n is the number of sides of the regular polygon.

Since, every interior angle of a regular polygon is equal,

Therefore, measure of each interior angle = [(n - 2) × 180º] / n

Thus, supplementary angle of an interior angle = 180º - measure of each interior angle

= 180º - [(n - 2) × 180º] / n

Thus, supplementary angle to any of the interior angles of a regular polygon is equal to 180º - [(n - 2) × 180º] / n.

What is the measure of the supplementary angle of an interior angle of a regular polygon?

Summary:

Supplementary angle to any of the interior angles of a regular polygon = 180º - [(n - 2) × 180º] / n.