How many sides does a regular polygon have if each of its interior angles is 1650?

By Ritesh|Updated : November 6th, 2022

A regular polygon with each of its interior angles 1650 has 24 sides. Finding the number of sides of a polygon using its exterior angle property:

We know that the measure of each interior angle is 1650

Then, each exterior angle = 1800 - 1650 [exterior angle = 1800 - interior angle]

= 150

(number of sides) x (a measure of each exterior angle) = 3600 (Using exterior angles property of polygons)

Number of sides x 150 = 3600

Number of sides = 3600/150 = 24

Properties of Regular Polygon

The following is a list of some of the regular polygons' attributes.

  1. A regular polygon has equal sides on all sides.
  2. There are no different interior angles.
  3. A regular polygon's perimeter is equal to the side measure multiplied by n.
  4. the total internal angles of a regular polygon or simple n-gon = (n − 2) × 180°
  5. The number of diagonals in a polygon with n sides = n(n – 3)/2
  6. The number of triangles formed by joining the diagonals from one corner of a polygon = n – 2
  7. The measure of each interior angle of n-sided regular polygon = [(n – 2) × 180°]/n
  8. The measure of each exterior angle of an n-sided regular polygon = 360°/n

Hence, a regular polygon with each of its interior angles 1650 has 24 sides

Summary:

How many sides does a regular polygon have if each of its interior angles is 1650?

A regular polygon has 24 sides with each of its interior angles 1650. Regular polygons are those that have the same internal angles and sides throughout. The equilateral triangle, square, and rhombus are a few examples of regular polygons.

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