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 remote interior angles. This is a fundamental theorem in Euclidean geometry.

2. How Does the Calculator Work?

The calculator applies the Exterior Angle Inequality Theorem:

Where:

• Exterior Angle — Angle formed by one side of the triangle and the extension of an adjacent side
• Interior Angle1, Interior Angle2 — The two non-adjacent interior angles (remote interior angles)

Explanation: The theorem holds true for all triangles in Euclidean geometry and helps establish many other geometric properties.

3. Importance of the Theorem

Details: This theorem is crucial for proving many other geometric theorems and for solving problems involving triangle angles. It helps establish relationships between exterior and interior angles.

4. Using the Calculator

Tips: Enter all three angle measures in degrees. The calculator will verify the inequalities and check if the angles form a valid triangle (sum of interior angles = 180°).

5. Frequently Asked Questions (FAQ)

Q1: Does this theorem apply to all triangles?
A: Yes, it applies to all triangles in Euclidean geometry.

Q2: What if the exterior angle equals an interior angle?
A: This would violate the theorem and indicate the figure is not a proper Euclidean triangle.

Q3: How is this related to the Exterior Angle Theorem?
A: The Exterior Angle Theorem states equality (exterior angle = sum of remote interiors), while this is an inequality version.

Q4: Can this be used for polygons other than triangles?
A: No, this specific theorem only applies to triangles, though similar concepts exist for other polygons.

Q5: What if the angles don't form a valid triangle?
A: The calculator will indicate "Invalid" in the Triangle Validity result.