Exterior Angle Theorem Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
An exterior angle of a triangle measures 140°140°. One of the remote interior angles is 75°75°. Find the other remote interior angle.

Solution

  1. 1
    Step 1: Exterior angle == sum of remote interior angles: 140°=75°+∠B140° = 75° + \angle B.
  2. 2
    Step 2: ∠B=140°−75°=65°\angle B = 140° - 75° = 65°.

Answer

The other remote interior angle is 65°65°.
Rearranging the Exterior Angle Theorem lets you find a missing remote interior angle by subtracting the known remote interior angle from the exterior angle. This is a straightforward application of the theorem in reverse.

About Exterior Angle Theorem

An exterior angle of a triangle equals the sum of the two non-adjacent (remote) interior angles.

Learn more about Exterior Angle Theorem →

More Exterior Angle Theorem Examples

Example 1 easy

In a triangle, two interior angles are [formula] and [formula]. An exterior angle is formed at the t

Example 2 medium

In [formula], the exterior angle at [formula] is [formula]. If [formula] and [formula], find the val

Example 4 hard

Prove that an exterior angle of a triangle is always greater than either of the two remote interior

← All Exterior Angle Theorem Examples Exterior Angle Theorem Concept