1. What is the Exterior Angle Theorem?

The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles (remote interior angles).

2. How Does the Calculator Work?

The calculator uses the Exterior Angle Theorem:

Where:

• \( \text{Interior Angle}_1 \) — First remote interior angle (degrees)
• \( \text{Interior Angle}_2 \) — Second remote interior angle (degrees)

Explanation: The theorem applies to any triangle and is fundamental in Euclidean geometry.

3. Importance of Exterior Angles

Details: Understanding exterior angles is crucial for solving many geometric problems, including polygon angle sums and parallel line theorems.

4. Using the Calculator

Tips: Enter two interior angles in degrees. Both values must be positive and their sum must be less than 180° (as they're part of a triangle).

5. Frequently Asked Questions (FAQ)

Q1: Does this work for all triangles?
A: Yes, the theorem applies to all triangles in Euclidean geometry.

Q2: What if my angles sum to 180° or more?
A: This would violate the triangle angle sum theorem (angles must sum to less than 180°).

Q3: Can I use this for polygons?
A: The theorem specifically applies to triangles, though similar concepts exist for polygons.

Q4: How is this different from adjacent angles?
A: An exterior angle is supplementary to its adjacent interior angle, but equal to the sum of the two remote interior angles.

Q5: Why is this theorem important?
A: It's fundamental for proving many other geometric theorems and solving practical problems.