Applications of the Exterior Angle Theorem

The applications of the exterior angle theorem are:

• To Find the Unknown Exterior Angles of Triangle
• To Find the Unknown Interior Angles of Triangle

Let’s discuss these cases in detail with the help of examples.

How to Find the Unknown Exterior Angles of Triangle?

To find the unknown exterior angle of the triangle we use the exterior angle theorem. If the value of two remote interior angles are given we can easily find the value of exterior angles.

Example: Given a triangle with an exterior angle and remote interior angles. The value of the two remote interior angles are 30° and 65°. Find the value of the exterior angle.

Solution:

By the exterior angle theorem

Exterior angle = sum of remote interior angles. ∠e = ∠i1 + ∠i2

⇒ The value of exterior angle = 30° + 65°

⇒ The value of exterior angle = 95°

How to Find the Unknown Interior Angles of Triangle?

To find the unknown exterior angle of the triangle we use the exterior angle theorem. If the value of two remote interior angles are given we can easily find the value of exterior angles.

Example: Given a triangle with an exterior angle and remote interior angles. The value of the one of the remote interior angles and exterior angle is are 80° and 165°. Find the value of the other remote interior angle.

Solution:

By the exterior angle theorem

Exterior angle = Sum of Remote Interior Angles.

⇒ ∠e = ∠i₁ + ∠i₂

⇒ 165° = 80° + ∠i₂

⇒ ∠i₂ = 165° – 80°

The value of other interior angle = 85°

Read More,

• Triangles in Geometry
• Types of Triangles
• Area of Triangle
• Triangle Inequality Theorem
• Congruence of Triangles
• Types of Angles

Exterior Angle Theorem is one of the foundational theorems in geometry, as it describes the relationship between exterior and interior angles in any triangle. An Exterior Angle is formed when any side of a polygon is extended to one side. In simple terms, an Exterior Angle is an angle that exists outside the boundaries of the polygon but shares a vertex with the polygon.

This article explores the relationship between the exterior angle and the remote angle of a triangle, i.e., the Exterior Angle Theorem. We will cover various topics related to the Exterior Angle Theorem, including its statement, proof, and some applications as well. Also, we will learn the Exterior Angle Inequality Theorem, as it is somewhat related to the Exterior Angle Theorem.