Triangle Angle Sum Math Example 3

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

Example 3

easy
Can a triangle have angles of 90°90°, 91°91°, and 1°1°? Justify your answer.

Solution

  1. 1
    Step 1: Add the three angles: 90°+91°+1°=182°90° + 91° + 1° = 182°.
  2. 2
    Step 2: Since 182°≠180°182° \neq 180°, this violates the Triangle Angle Sum Theorem.

Answer

No. The angles sum to 182°182°, not 180°180°, so this is not a valid triangle.
The Triangle Angle Sum Theorem is an exact rule: the interior angles of any triangle must sum to exactly 180°. Any triple of positive angles that does not total 180° cannot form a triangle. This is also useful for checking whether given angle measures are valid.

About Triangle Angle Sum

The three interior angles of any triangle always sum to exactly 180°180°, so knowing two angles determines the third.

Learn more about Triangle Angle Sum →

More Triangle Angle Sum Examples

Example 1 easy

A triangle has angles [formula] and [formula]. Find the third angle.

Example 2 medium

In an isosceles triangle, the vertex angle is [formula]. Find the two base angles.

Example 4 hard

In [formula], [formula], [formula], [formula]. Find all three angles.

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