What is an Exterior Angle Theorem?
The exterior angle theorem is Proposition 1.16 in Euclid's Elements, which states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles. This is a fundamental result in absolute geometry because its proof does not depend upon the parallel postulate.
Small Explanation:
- When a triangle's side is extended, the resultant exterior angle formed is equal to the sum of the measures of the two opposite interior angles of the triangle.
- The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
What is the Exterior Angle Theorem Formula?
The exterior angle theorem tells us that any exterior angle of a triangle equals the sum of the opposite two interior angles and that the sum of all three interior angles of a triangle equals 180° , the sum of two right angles (triangle sum theorem).
How do you use the Exterior Angle Theorem?
To use the exterior angle theorem in a triangle we first need to identify the exterior angle and then the associated two remote interior angles of the triangle. A common mistake of considering the adjacent interior angle should be avoided. After identifying the exterior angles and the related interior angles, we can apply the formula to find the missing angles or to establish a relationship between sides and angles in a triangle.
