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. This calculator simplifies the relationship by calculating the adjacent interior angle.

2. How Does the Calculator Work?

The calculator uses the simple relationship:

Where:

• Exterior Angle — Angle formed by one side of the triangle and the extension of an adjacent side
• Interior Angle — Angle inside the triangle adjacent to the exterior angle

Explanation: The sum of an exterior angle and its adjacent interior angle is always 180° (they form a linear pair).

3. Importance of Angle Calculation

Details: Understanding exterior angles is crucial in geometry for solving triangle problems, proving theorems, and in practical applications like architecture and engineering.

4. Using the Calculator

Tips: Enter the exterior angle in degrees (must be between 0° and 360°). The calculator will compute the adjacent interior angle.

5. Frequently Asked Questions (FAQ)

Q1: Can an exterior angle be more than 180°?
A: Yes, in concave polygons, but in triangles exterior angles are always between 0° and 360°.

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

Q3: How is this different from interior angles?
A: Interior angles are inside the triangle, while exterior angles are formed outside.

Q4: Can this calculator work for other polygons?
A: This specific calculator is designed for triangles, but the concept can be extended to other polygons.

Q5: Why is 180° significant here?
A: Because an exterior angle and its adjacent interior angle form a straight line (180°).