Question

how many sides does a regular polygon have if each of its interior angles is 165°​

Answer 1

Answer:

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

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Answer 2

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Interior angle of the given polygon: 165°

⟶ Exterior angle of polygon: 180°-165°= 15°

We know that:

⟶ Sum of any exterior angle of the polygon is: 360°

⟶ Number of sides in regular polygon:

360/15

= 24

Therefore, The number of sides in regular polygon is 24.