Exterior Angles of a Triangle Calculator
Find exterior angles from valid triangle inputs quickly. Check totals, missing values, and theorem consistency. Study patterns, save reports, and compare sample triangle cases.
Calculator Input
Enter any two or three interior angles. The calculator finds each simple exterior angle and verifies triangle angle rules.
Example Data Table
| Triangle | Interior A | Interior B | Interior C | Exterior A | Exterior B | Exterior C | Exterior Sum |
|---|---|---|---|---|---|---|---|
| Equiangular | 60° | 60° | 60° | 120° | 120° | 120° | 360° |
| Right Triangle | 90° | 35° | 55° | 90° | 145° | 125° | 360° |
| Obtuse Triangle | 110° | 30° | 40° | 70° | 150° | 140° | 360° |
Formula Used
- Simple exterior angle: Exterior = 180° − Interior
- Missing interior angle: Missing = 180° − (other two interior angles)
- Exterior angle theorem: Exterior at one vertex = sum of the two remote interior angles
- Total exterior sum: Exterior A + Exterior B + Exterior C = 360°
- Reflex exterior angle: Reflex Exterior = 360° − Simple Exterior
How to Use This Calculator
- Type a triangle name for easier exports.
- Enter any two or all three interior angles.
- Leave one angle blank if you want auto-computation.
- Select your preferred decimal precision.
- Choose a graph mode for the visual output.
- Press the calculate button to generate results.
- Review the angle table, theorem check, and graph.
- Download the report as CSV or PDF.
Frequently Asked Questions
1. What is an exterior angle of a triangle?
It is the outside angle formed when one side extends beyond a vertex. Each simple exterior angle forms a straight line with its matching interior angle.
2. How do I calculate one exterior angle?
Subtract the interior angle from 180°. For example, if the interior angle is 52°, the simple exterior angle is 128°.
3. Why do the exterior angles always total 360°?
A full turn around any polygon equals 360°. Walking around a triangle adds one exterior turn at each vertex, so their total is always 360°.
4. Can I enter only two interior angles?
Yes. The calculator finds the missing interior angle using the 180° triangle rule, then computes all exterior angles automatically.
5. What is the exterior angle theorem?
It states that one exterior angle equals the sum of the two remote interior angles. This gives a quick way to verify triangle angle consistency.
6. What is the difference between simple and reflex exterior angles?
The simple exterior angle is supplementary to the interior angle. The reflex exterior angle is the larger outside turn, equal to 360° minus the simple exterior angle.
7. Why does the calculator reject some inputs?
Triangle interior angles must each stay between 0° and 180°. Their total must also equal 180°, otherwise the triangle is invalid.
8. Who can use this calculator?
Students, teachers, parents, tutors, and exam learners can use it for homework checks, lesson demonstrations, and quick theorem verification.