1. What is the Exterior Angle Inequality Theorem?

The Exterior Angle Inequality Theorem states that the measure of an exterior angle of a triangle is greater than the measure of either of its two non-adjacent (remote) interior angles. This is a fundamental theorem in Euclidean geometry.

2. How Does the Calculator Work?

The calculator verifies the theorem by comparing the exterior angle with each remote interior angle:

It also calculates the sum of the two interior angles to help verify triangle angle properties.

3. Importance of the Theorem

Details: This theorem is crucial in geometry proofs and helps establish relationships between angles in triangles. It's often used to prove other geometric theorems and solve problems involving triangle angles.

4. Using the Calculator

Tips: Enter all three angle measures in degrees. The calculator will verify the theorem and show whether the exterior angle is greater than each interior angle. Valid angle measures should be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is an exterior angle of a triangle?
A: An exterior angle is formed by one side of the triangle and the extension of an adjacent side.

Q2: What are remote interior angles?
A: These are the two non-adjacent interior angles of the triangle that don't share a vertex with the exterior angle.

Q3: Is the exterior angle equal to the sum of remote interior angles?
A: Yes, by the Exterior Angle Theorem (not inequality), the exterior angle equals the sum of the two remote interior angles.

Q4: Does this apply to all polygons?
A: No, this specific theorem applies only to triangles. Other polygons have different angle relationships.

Q5: What if the angles don't satisfy the theorem?
A: Then they don't represent valid exterior and interior angles of a triangle, or there may be measurement errors.