Exterior Angle Theorem Math Example 1

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Example 1

easy
In a triangle, two interior angles are 65°65° and 48°48°. An exterior angle is formed at the third vertex. Find the exterior angle.

Solution

  1. 1
    Step 1: The Exterior Angle Theorem states: an exterior angle of a triangle equals the sum of the two non-adjacent (remote) interior angles.
  2. 2
    Step 2: The two remote interior angles are 65°65° and 48°48°.
  3. 3
    Step 3: Exterior angle =65°+48°=113°= 65° + 48° = 113°.

Answer

The exterior angle is 113°113°.
The Exterior Angle Theorem provides a shortcut: instead of finding the third interior angle first (180°−65°−48°=67°180° - 65° - 48° = 67°) and then its supplement (180°−67°=113°180° - 67° = 113°), you directly add the two remote interior angles. Both methods give the same answer because they both reduce to the same algebra.

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 2 medium

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

Example 3 easy

An exterior angle of a triangle measures [formula]. One of the remote interior angles is [formula].

Example 4 hard

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

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