Question

an interior angle of a regular polygon has a measure of 135° how many sides does it have

Answer 1

8 sides

the exterior angle = 180° - 135° = 45° ( exterior/ interior are supplementary )

the sum of the exterior angles of a polygon = 360°

number of sides = $\frac{360}{45}$ = 8

Answer 2

The regular polygon mentioned has 8 sides.

What is a polygon?

"A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain."

Given, an interior angle of a regular polygon is 135°.

Let, there are 'n' sides of that regular polygon.

Therefore, sum of the interior angles of that polygon = n × 135°.

Again, sum of the interior angles of any polygon with 'n' sides

= (n - 2) × 180°.

Therefore, n × 135° = (n - 2) × 180°

⇒ (180° - 135°)n = 360°

⇒ n = $\frac{360}{45}$

⇒ n = 8

Therefore, the regular polygon has 8 sides.

Learn more about a polygon here: https://brainly.com/question/4209410

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