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Triangle Interior and Exterior Angle Relationships

No. Each exterior is the nonreflex supplement of its adjacent interior. Interiors sum to 180 degrees and these exteriors sum to 360 degrees. Enter two interiors or an interior plus a nonadjacent exterior for all fields; two exteriors produce only the third exterior.

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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.

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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: a 30, b 60 gives c 90, d 90, e 120, f 150.

A+B+C = π; D = π−C; E = π−B; F = π−A

Worked example

Enter these known values and leave the other values blank.

a
30 deg
b
60 deg
c
90 deg
d
90 deg
e
120 deg
f
150 deg

Assumptions and limitations

  • Interior angles are positive and sum to one half-turn. Each entered exterior angle is the nonreflex supplement at the corresponding vertex. Two independent compatible angles determine the remaining relationships; all three exterior angles total one full turn. Enter two interior angles, or an interior and a nonadjacent exterior angle, to solve all six. In the retained solver, two exterior angles produce the third exterior only; they do not populate the interior fields.
  • Use compatible units and enough independent values. Clear unknowns before solving backward. Original reference drawings are schematic and do not scale to entered values.

Common questions

Are exterior angles reflex angles here?

No. Each exterior is the nonreflex supplement of its adjacent interior. Interiors sum to 180 degrees and these exteriors sum to 360 degrees. Enter two interiors or an interior plus a nonadjacent exterior for all fields; two exteriors produce only the third exterior.

References

Use exact π angle boundaries and valid geometric bounds for the documented model; rounded π ceilings can incorrectly reject near-straight valid triangles.

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