Exterior Angles Of A Polygon

You are already aware of the term polygon. A polygon is a flat figure that is made up of three or more line segments and is enclosed. The line segments are called the sides and the point where two sides meet is called the vertex of the polygon. The pair of sides that meet at the same vertex are called adjacent sides. An angle at one of the vertices is called the interior angle. In this article, we will discuss exterior angles of polygons.

What are Exterior Angles?

An exterior angle is an angle which is formed by one of its sides and the extension of its adjacent side.

Exterior Angles Of A Polygon

  • They are formed on the outside or exterior of the polygon.
  • The sum of an interior angle and its corresponding exterior angle is always 180 degrees since they lie on the same straight line.
  • In the figure, angles 1, 2, 3, 4 and 5 are the exterior angles of the polygon.

Sum of the Exterior Angles of a Polygon

Let us say you start travelling from the vertex at angle 1. You go in a clockwise direction, make turns through angles 2, 3, 4 and 5 and come back to the same vertex. You covered the entire perimeter of the polygon and in fact, made one complete turn in the process. One complete turn is equal to 360 degrees. Thus, it can be said that ∠1, ∠2, ∠3, ∠4 and ∠5 sum up to 360 degrees.

Hence, the sum of the measures of the exterior angles of a polygon is equal to 360 degrees, irrespective of the number of sides in the polygons.

Problem Statement:

Example: In the given figure, find the value of x.

Exterior Angles Of A Polygon

Solution: We know that the sum of exterior angles of a polygon is 360 degrees.

Thus, 70° + 60° + 65° + 40° + x = 360°

235° + x = 360°

X = 360° – 235° = 125°

Example: Identify the type of regular polygon whose exterior angle measures 120 degrees.

Solution: Since the polygon is regular, the measure of all the interior angles is the same. Therefore, all its exterior angles measure the same as well, that is, 120 degrees.

Since the sum of exterior angles is 360 degrees and each one measures 120 degrees, we have,

Number of angles = 360/120 = 3

Since the polygon has 3 exterior angles, it has 3 sides. Hence it is an equilateral triangle.


Practise This Question

If a regular polygon has n sides, then the sum of its exterior angles is