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Triangle Exterior Angles and Supplementary Interiors

Enter two interiors, or an interior and a nonadjacent exterior. Adjacent interior/exterior angles are dependent supplements. Two exterior inputs populate the third exterior only in this retained solver.

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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: 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 a, b and c are positive and sum to 180°. The adjacent nonreflex exterior angles d, e and f are their supplements, not arbitrary reflex turning angles. The three exterior angles sum to 360°. 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

Which two angles populate all six angle fields?

Enter two interiors, or an interior and a nonadjacent exterior. Adjacent interior/exterior angles are dependent supplements. Two exterior inputs populate the third exterior only in this retained solver.

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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