Free · Triangle calculators 🔺

Triangle Interior Angles: Find the Third

Find a missing interior angle of a plane triangle in degrees or radians.

  • Formula & worked example
  • Private in your browser
  • No signup
Go to tool

Calculator inputs

Loading calculator…

How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A triangle with angles 47° and 68° has a third angle of 65°, since its three interior angles total 180°.

α + β + γ = 180° = π radians

Worked example

Enter these known values and leave the other values blank.

First interior angle
47 deg
Second interior angle
68 deg
Third interior angle
65 deg

Assumptions and limitations

  • This is a nondegenerate triangle in Euclidean plane geometry. Each angle must be greater than 0 and less than 180°.
  • The two entered angles must add to less than 180°. Angle units can be selected separately.
  • Three angles fix the shape up to similarity, but do not determine side lengths or area without a length scale.

Common questions

Can three angles determine the side lengths?

No. Similar triangles can have the same three angles and different side lengths. Supply a length measurement to establish size.

Why is a zero third angle invalid?

If the other angles already total 180°, the remaining angle is zero. That describes a degenerate shape rather than a triangle with positive interior angles.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

Explore triangle calculators 🔺 or browse all math calculators.