Triangle Sum and Exterior Angle Theorem Calculator

Find missing angles and verify triangle rules. Explore interior and exterior relationships using graphs steps. This calculator makes theorem practice clearer for every student.

Calculator Inputs

Interior Angle A (°)

Interior Angle B (°)

Interior Angle C (°)

Exterior Angle A (°)

Exterior Angle B (°)

Exterior Angle C (°)

Decimal Precision

Plotly Graph

The graph compares solved interior and exterior angles for vertices A, B, and C.

Example Data Table

Case	Known Inputs	Computed Result	Main Rule Used
Example 1	A = 50°, B = 60°	C = 70°, Exterior C = 110°	Triangle sum and supplementary relationship
Example 2	B = 45°, Exterior A = 125°	C = 80°, A = 55°	Exterior angle theorem
Example 3	A = 90°, C = 35°	B = 55°, Exterior B = 125°	Triangle sum then linear pair

Formula Used

Triangle Sum Theorem: A + B + C = 180°

Missing Interior Angle: Missing = 180° - (other two interior angles)

Exterior Angle Theorem: Exterior A = B + C, Exterior B = A + C, Exterior C = A + B

Linear Pair Rule: Interior + Adjacent Exterior = 180°

The calculator uses these relationships repeatedly until no new angle can be solved from the provided information.

How to Use This Calculator

Enter any known interior angles, exterior angles, or both.
Choose the decimal precision you want for results.
Press Calculate Triangle Angles.
Review the solved angles, theorem checks, and triangle classification.
Use the chart to compare interior and exterior values visually.
Download the solved results as CSV or PDF when needed.

FAQs

1. What does the triangle sum theorem say?

It states that the three interior angles of any triangle add to 180 degrees. If two interior angles are known, subtract their sum from 180 to find the third.

2. What does the exterior angle theorem say?

An exterior angle equals the sum of the two remote interior angles. This rule helps solve unknown angles without measuring every angle directly.

3. Can I enter exterior angles only?

Yes, when the exterior values are valid and sufficient. The calculator converts each known exterior angle into its adjacent interior angle using the 180 degree linear pair relationship.

4. Why does the calculator show a consistency warning?

Warnings appear when the entered angles conflict with triangle rules. For example, an interior and exterior pair may not total 180 degrees, or the three interior angles may not total 180.

5. Can this calculator classify the triangle?

Yes. If all interior angles are solved and valid, it labels the triangle by angle type, such as acute, right, or obtuse, and by side pattern, such as scalene or isosceles.

6. What range is allowed for each angle?

Each interior or adjacent exterior angle must be greater than 0 and less than 180 degrees. Values outside that range cannot represent a standard triangle angle pair.

7. What does the graph show?

The Plotly chart displays the solved interior and exterior angles for vertices A, B, and C. It makes comparisons faster and helps confirm theorem relationships visually.

8. When should I download CSV or PDF results?

Use CSV for spreadsheets, records, or class data analysis. Use PDF when you want a clean report for printing, sharing, or attaching to homework and notes.