Calculator Inputs
Formula Used
Exterior angle = 180° − adjacent interior angle
Exterior angle = remote interior angle 1 + remote interior angle 2
Interior A + Interior B + Interior C = 180°
Exterior A + Exterior B + Exterior C = 360°
The calculator applies these relationships depending on the method you choose. If you know one adjacent interior angle, it finds the supplementary exterior. If you know the two remote interior angles, it adds them using the theorem. If all three interior angles are known, it computes every exterior angle and validates the full triangle.
How to Use This Calculator
- Select the calculation method that fits your geometry problem.
- Choose the vertex label if you want the result tied to A, B, or C.
- Enter the known angle values in degrees.
- Pick how many decimal places you want in the answer.
- Click Calculate Exterior Angle to show the result above the form.
- Review the detailed table, theorem checks, and chart.
- Use the CSV or PDF buttons to export the current result.
Example Data Table
| Case | Given Data | Exterior Angle | Check |
|---|---|---|---|
| 1 | Adjacent interior = 68° | 112° | 68° + 112° = 180° |
| 2 | Remote interiors = 54°, 61° | 115° | 54° + 61° = 115° |
| 3 | Interior angles = 45°, 55°, 80° | Exterior at A = 135° | All exteriors total 360° |
| 4 | Adjacent interior = 97.5° | 82.5° | Supplementary pair confirmed |
| 5 | Remote interiors = 72°, 38° | 110° | Theorem matches exactly |
Frequently Asked Questions
1) How to find exterior angles of a triangle?
Subtract the adjacent interior angle from 180°, or add the two remote interior angles. Both methods give the same exterior angle at the selected vertex.
2) Worksheet triangle sum and exterior angle theorem
On worksheets, first verify the interior angles total 180°. Then use exterior angle = sum of the two remote interiors, or use 180° minus the adjacent interior.
3) Triangle exterior angle theorem
The theorem says an exterior angle of a triangle equals the sum of the two non-adjacent interior angles. It is a fast way to solve missing angle problems.
4) What is the sum of the exterior angles of a triangle?
One exterior angle at each vertex always adds up to 360°. This remains true for every triangle, regardless of side lengths or angle sizes.
5) Can an exterior angle of a triangle be greater than 180°?
In standard school geometry, the exterior angle formed with a straight extension is less than 180°. It is supplementary to the adjacent interior angle.
6) Do all triangles have three exterior angles?
Yes. Each vertex can form an exterior angle by extending one side. If you choose one exterior at each vertex, their sum is 360°.
7) What happens if the interior angles do not total 180°?
Then the values do not describe a valid triangle in ordinary Euclidean geometry. Check the inputs for typing errors or wrong problem data.
8) Why does an exterior angle equal the two remote interiors?
The adjacent interior and exterior form 180°. Since all interior angles sum to 180°, the exterior must match the other two interior angles combined.