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# 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.

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