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 (remote) interior angles. This fundamental geometric principle helps in solving various triangle-related problems.

2. How Does the Calculator Work?

The calculator uses the Exterior Angle Theorem formula:

Where:

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

Explanation: The theorem applies to any triangle and is useful for finding missing angle measures in geometric problems.

3. Importance of the Theorem

Details: Understanding this theorem is essential for geometry students and professionals working with triangular structures in engineering, architecture, and design.

4. Using the Calculator

Tips: Enter two non-adjacent interior angles of a triangle (both must be greater than 0° and their sum must be less than 180°).

5. Frequently Asked Questions (FAQ)

Q1: Does this work for all triangles?
A: Yes, the theorem applies to all triangles, whether scalene, isosceles, or equilateral.

Q2: What's the maximum possible exterior angle?
A: The exterior angle must be less than 180° (since interior angles sum to 180°).

Q3: Can I use this for polygons other than triangles?
A: No, this specific theorem only applies to triangles, though similar concepts exist for other polygons.

Q4: How is this different from the Triangle Sum Theorem?
A: The Triangle Sum Theorem states interior angles sum to 180°, while this theorem relates an exterior angle to two interior angles.

Q5: What if my angles sum to 180° or more?
A: This would violate triangle properties - the calculator will show no result for invalid inputs.