Triangle Angle Sum Math Example 1

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

Example 1

easy
A triangle has angles 55°55° and 72°72°. Find the third angle.

Solution

  1. 1
    Step 1: Recall the Triangle Angle Sum Theorem: the three interior angles of any triangle sum to 180°180°.
  2. 2
    Step 2: Let the third angle be xx. Then 55°+72°+x=180°55° + 72° + x = 180°.
  3. 3
    Step 3: Solve: x=180°−55°−72°=180°−127°=53°x = 180° - 55° - 72° = 180° - 127° = 53°.

Answer

The third angle is 53°53°.
The Triangle Angle Sum Theorem states that the interior angles of every triangle add to exactly 180°. This holds for all triangles — acute, right, and obtuse. To find a missing angle, subtract the sum of the known angles from 180°.

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 2 medium

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

Example 3 easy

Can a triangle have angles of [formula], [formula], and [formula]? Justify your answer.

Example 4 hard

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

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