1. What Are Exterior Angles of a Triangle?

An exterior angle of a triangle is formed by extending one side of the triangle. The measure of an exterior angle equals the sum of the two non-adjacent interior angles, or equivalently, 180° minus the adjacent interior angle.

2. How Does the Calculator Work?

The calculator uses the exterior angle formula:

For each of the three interior angles of a triangle, the corresponding exterior angle is calculated by subtracting the interior angle from 180°.

3. Properties of Exterior Angles

Key Properties:

• The sum of all three exterior angles of a triangle is 360°
• Each exterior angle is supplementary to its adjacent interior angle
• An exterior angle equals the sum of the two opposite interior angles

4. Using the Calculator

Instructions: Enter all three interior angles of a triangle (must sum to 180°). The calculator will display the three corresponding exterior angles.

5. Frequently Asked Questions (FAQ)

Q1: Why must the angles sum to 180°?
A: This is a fundamental property of triangles in Euclidean geometry. The sum of interior angles in any triangle is always 180°.

Q2: What if my angles don't sum to 180°?
A: The calculator will show an error. Double-check your angle measurements as they may be incorrect.

Q3: Can I use this for other polygons?
A: The exterior angle concept applies to all polygons, but the calculation differs. For an n-sided polygon, the sum of exterior angles is always 360°.

Q4: What are exterior angles used for?
A: Exterior angles are important in geometry proofs, architectural design, and various engineering applications.

Q5: Do exterior angles apply to spherical triangles?
A: No, these properties only apply to planar (flat) triangles. Spherical triangles have different angle sum properties.