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

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.

## Answer: It is a regular octagon that has an interior angle of 135°.

Let's see the solution step by step.

**Explanation:**

We have to find, the number of sides of the polygon.

The formula for the interior angle of a regular polygon with n sides is,

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.

Hence, the polygon that has 8 sides is called an octagon.

The figure of a regular octagon is given below: