# Exterior Angle Inequality Proof with Euclidean Illustration

## Exterior Angle Inequality Proof

Here we provide a proof of the Exterior Angle Inequality, which says that the measure of an exterior angle of a triangle is greater than the measures of each of its remote interior angles. This theorem is valid in Euclidean and Hyperbolic Geometries. With a further restriction to small enough triangles, it is also valid in Spherical Geometry, even though it is false in general in Spherical Geometry. The illustration in Euclidean Geometry is dynamic, but the Hyperbolic and Spherical illustrations are static. There are additional dynamic illustrations in those geometries available as separate activities.
In Euclidean Geometry, there is an even stronger result: The measure of an exterior angle is equal to the sum of the measures of its remote interior angles.

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