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

By BYJU'S Exam Prep

Updated on: September 25th, 2023

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

Table of content

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

Properties of Regular Polygon

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

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