Calculator
Enter any two interior angles of a valid triangle. The calculator subtracts their sum from the triangle total and then checks the completed angle set.
Plotly Graph
The chart displays the angle share of the completed triangle. It updates after each valid calculation.
Example Data Table
These examples show how the missing interior angle changes when two angles are already known.
| Case | Angle A | Angle B | Third Angle | Classification |
|---|---|---|---|---|
| Lab sketch 1 | 35° | 65° | 80° | Acute triangle |
| Force diagram | 45° | 45° | 90° | Right triangle |
| Wave path | 30° | 110° | 40° | Obtuse triangle |
| Prism sketch | 60° | 60° | 60° | Equiangular triangle |
| Vector triangle | 25° | 85° | 70° | Acute triangle |
Formula Used
For every Euclidean triangle, the sum of the three interior angles is constant. That constant is 180° in degree mode or π in radian mode.
Degree formula: Third Angle = 180° − (Angle A + Angle B)
Radian formula: Third Angle = π − (Angle A + Angle B)
This rule is useful in physics diagrams because triangular relationships appear in vector addition, optics paths, force decomposition, and geometric sketches used during measurements. Once two interior angles are known, the third value is fixed. The calculator also checks whether the finished triangle is acute, right, obtuse, equiangular, isosceles by angles, or scalene by angles.
A valid result requires three positive interior angles. If the first two entries already equal or exceed the triangle total, no real triangle can be formed. That is why the calculator validates the sum before showing the final answer.
How to Use This Calculator
- Enter the first known interior angle in Angle A.
- Enter the second known interior angle in Angle B.
- Select degrees or radians.
- Choose the decimal precision you want in the output.
- Press Calculate Third Angle.
- Read the result box placed above the form.
- Review the classification, step list, and chart.
- Use the CSV or PDF button if you want a saved copy.
Frequently Asked Questions
1. Why is the third angle found by subtraction?
Because the interior angles of a triangle always add to 180° in degree mode. The unknown angle is the remaining part after subtracting the two known angles.
2. Can this calculator work in radians?
Yes. Switch the unit to radians and the calculator uses π as the full triangle angle total. The same subtraction idea still applies.
3. What happens if my two angles add to 180° or more?
That input cannot form a valid triangle. A real triangle needs three positive interior angles, so the first two must leave room for a positive third angle.
4. Does it work for right triangles?
Yes. If one completed angle becomes 90°, the calculator marks the shape as a right triangle. For example, 45° and 45° produce a third angle of 90°.
5. Why does the calculator show triangle classification?
Classification helps you interpret the result faster. It tells you whether the finished triangle is acute, right, obtuse, equiangular, isosceles by angles, or scalene by angles.
6. Can rounding change the displayed answer?
Yes, only the displayed form changes when you change decimal precision. The calculation uses the entered numeric values first, then formats the visible result afterward.
7. Is this useful in physics work?
Yes. Triangle angles appear in vector diagrams, reflected paths, component sketches, and many classroom geometry setups used to model physical relationships.
8. Do I need side lengths to use this tool?
No. This calculator only needs two interior angles. The third interior angle depends on the triangle angle-sum rule, not on side-length measurements.