Question

A regular polygon has an interior angle of 165 degrees. How many sides does it have?

Answer 1

Hello, 24

Explanation:

Ingerior angle = 165

Exterior angle = 180 - 165 = 15

The sum of exterior angles of any polygon is 360

Number of sides = 360/15 = 24 A polygon is any two dimensional shape formed with the straight lines. Triangles, pentagons, quadrilaterals, and hexagons are all examples of the polygons. The name itself tells as to how many sides the shape has. For example, a triangle has three sides, whereas a quadrilateral has four sides.

Thus, when the regular polygon have if each of its interior angle is 165° then,

The corresponding exterior angle must be 180-165 = 15°

The sum of ALL the exterior angles is 360°

Sides of exterior angles is 360/15 = 24

Therefore the number of sides a regular polygon will have is 24 Have a Awesome Day!

Answer 2

24

Explanation:

First find the exterior angle: 180 - 165 = 15

Then 360 ÷ 15 because 360 divided by he exterior angle of a regular polygon is equal to the number of sides.