1. What is the Triangle Exterior Angle Theorem?

The Triangle 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. Alternatively, it can be calculated as 180° minus the adjacent interior angle.

2. How Does the Calculator Work?

The calculator uses the simple formula:

Where:

• \( Interior \) — The interior angle adjacent to the exterior angle (degrees)
• \( Exterior \) — The resulting exterior angle (degrees)

Explanation: Since the interior and exterior angles form a linear pair, they are supplementary (add up to 180°).

3. Importance of Exterior Angle Calculation

Details: Calculating exterior angles is fundamental in geometry for solving triangle problems, proving theorems, and understanding polygon properties. Exterior angles are crucial in various geometric constructions and proofs.

4. Using the Calculator

Tips: Enter the interior angle in degrees. The value must be between 0 and 180 degrees (exclusive). The calculator will compute the corresponding exterior angle.

5. Frequently Asked Questions (FAQ)

Q1: What is an exterior angle of a triangle?
A: An exterior angle is formed by extending one side of the triangle. It lies outside the triangle and is adjacent to an interior angle.

Q2: Can an exterior angle be greater than 180°?
A: No, in a triangle, exterior angles are always between 0° and 180° (but not including 0° or 180°).

Q3: What is the sum of all exterior angles of a triangle?
A: The sum of all exterior angles (one at each vertex) of any convex polygon, including triangles, is always 360°.

Q4: How is this different from interior angles?
A: Interior angles are inside the triangle and sum to 180°, while exterior angles are outside and each is supplementary to its adjacent interior angle.

Q5: Can this calculator be used for other polygons?
A: This specific calculator is designed for triangles. Other polygons have different relationships between interior and exterior angles.