Exterior Angles Of A Triangle

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In this lesson, we will learn
• about exterior angles of triangles
• how to find the unknown exterior angle of a triangle
• how to prove that the sum of exterior angles of a triangle is 360°

Exterior Angles of a Triangle

An exterior angle of a triangle is formed by any side of a triangle and the extension of its adjacent side.

The Exterior Angle Theorem states that

An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Example :

Find the values of x and y in the following triangle.

Solution:

x + 50° = 92° (sum of opposite interior angles = exterior angle)

x = 92° – 50° = 42°

y + 92° = 180° (interior angle + adjacent exterior angle = 180°.)

y = 180° – 92° = 88°

The following video gives a definition of exterior angles and shows how to find the unknown exterior angle of a triangle

The following video shows an example of how to find the exterior angle of a triangle.
This video will define the interior and exterior angles of a triangle and then state several theorems involving the interior and exterior angles of a triangle.

Sum of Exterior Angles of a Triangle

This video provides a two column proof of the sum of the exterior angles of a triangle is 360 degree.

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