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 formula:

Where:

• Interior Angle1 — First non-adjacent interior angle (degrees)
• Interior Angle2 — Second non-adjacent interior angle (degrees)

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

3. Importance of Exterior Angle Calculation

Details: Understanding exterior angles is crucial for solving various geometric problems, proving theorems, and analyzing polygon properties.

4. Using the Calculator

Tips: Enter both interior angles in degrees. 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 theorem apply to all triangles?
A: Yes, the exterior angle theorem applies to all triangles in Euclidean geometry.

Q2: What's the sum of all exterior angles of a triangle?
A: The sum of all exterior angles (one at each vertex) is always 360°.

Q3: Can an exterior angle be equal to an interior angle?
A: Yes, in a right-angled triangle, the exterior angle adjacent to the right angle equals the right angle (90°).

Q4: How is this related to polygon exterior angles?
A: This is a specific case of the general polygon exterior angle concept.

Q5: What if my angles sum to 180° or more?
A: The calculator will not display a result as this would violate the triangle angle sum theorem.