Free · Triangle calculators 🔺

Triangle Interior Angle Sum and Missing Angle

This tool uses planar Euclidean geometry. Curved-surface triangles can have a different interior angle sum.

  • Formula & worked example
  • Private in your browser
  • No signup
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Calculator inputs

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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

Example in initial displayed units: Angle α 30, Angle β 60 gives Angle γ 90.

α+β+γ = π radians = 180°

Worked example

Enter these known values and leave the other values blank.

Angle α
30 deg
Angle β
60 deg
Angle γ
90 deg

Assumptions and limitations

  • The three interior angles describe a nondegenerate Euclidean triangle. Each is positive and less than 180 degrees. Enter two compatible angles and leave the third empty; the entered pair must total less than 180 degrees. The angle controls retain degrees, radians and other captured units.
  • Clear unknown measurements before solving backward. Use compatible units and independent values. Reference pictures are original schematic drawings. Independently rounded measurements can fail strict compatibility at a boundary.

Common questions

Does this apply to a triangle drawn on a sphere?

This tool uses planar Euclidean geometry. Curved-surface triangles can have a different interior angle sum.

How do I use this calculator with different units?

Select the unit beside each measure. Length, squared length and volume use different dimensions; changing a unit preserves the physical value. Compound length controls represent feet/inches or meters/centimeters together.

References

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

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