Question

Find the number of sides of a regular polygon if each of its interior angles is 165°

Answer 1

Given :-

• Interior angle = 165°

To Find :-

• Number of sides of a regular polygon.

Solution :-

Exterior angle :-

$:\implies\sf{180-Interior\:angle}$

$:\implies\sf{180-165}$

$:\implies\sf{15°}$

∴ Exterior angle = 15°.

Number of side :-

$:\implies\sf{Number\:of\:sides=\dfrac{360}{Exterior\:angle}}$

$:\implies\sf{Number\:of\:sides=\dfrac{360}{15}}$

$\sf:\implies \underline{\boxed{\pink{\mathfrak{Number\:of\:sides=24}}}}$

∴ Number of sides of the polygon = 24

$\large\frak{\underline{\underline{\green{More\:To\:Know:-}}}}$

• 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.

Answer 2

24 sides

Step-by-step explanation:

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