An interior angle of a regular polygon has a measure of 135°. What type of polygon is it?

Solution:

Given an interior angle of a polygon is 135°. 

In mathematics, according to Euclidean Geometry, a polygon that has all sides of the same length and all angles of the same measure is called a regular polygon.

We know that each of all angles of a polygon whose sides and angles are equal is given by (n - 2) × 180°/n, where n is the number of sides.

Interior angle = [(n - 2) × 180] / n.

Applying the interior angle = 135° in the formula, we get

135° = ((n - 2) × 180) / n

⇒ 135 × n = [(n - 2) × 180]

⇒ 135 × n = 180n - 360

⇒ 180n - 135n = 360

⇒ 45n = 360

⇒ n = 360 / 45

⇒ n =  8.  

We know that the polygon that has 8 sides is called an octagon.

An interior angle of a regular polygon has a measure of 135°. What type of polygon is it?

Summary:

An interior angle of a regular polygon has a measure of 135°, it is an octagon.