## Exterior Angle Inequality Theorem

### The Exterior Angle Inequality Theorem is a geometric theorem that relates the measures of the exterior angles of a triangle to the measures of its interior angles

The Exterior Angle Inequality Theorem is a geometric theorem that relates the measures of the exterior angles of a triangle to the measures of its interior angles.

The theorem states that the measure of an exterior angle of a triangle is greater than the measure of either of its corresponding remote interior angles.

To understand this concept, let’s consider a triangle ABC. The exterior angle at vertex C is formed by extending one side of the triangle, say side AB, beyond the vertex C. This exterior angle is denoted as ∠ACB.

The Exterior Angle Inequality Theorem states that:

– The measure of ∠ACB is greater than the measure of ∠A (the remote interior angle at vertex A).

– The measure of ∠ACB is greater than the measure of ∠B (the remote interior angle at vertex B).

Mathematically, the theorem can be expressed as follows:

∠ACB > ∠A and ∠ACB > ∠B.

This theorem is handy when solving problems involving the measures of angles in triangles. It enables us to establish relationships and make comparisons between the interior and exterior angles of a triangle.

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