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(polygon) that has an interior angle of 135°.
Let's see the solution step by step.
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.
We know that the polygon that has 8 sides is called an octagon.
The figure of a regular octagon is given below: