# Exterior Angles Of A Triangle

In these 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°

The following diagrams give the theorems involving the exterior angles of triangles. Scroll down the page for more examples and solutions.

### 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°

What is an exterior angle and how to find the unknown exterior angle of a triangle?

The angles on a straight line add up to 180°.
The interior angles of a triangle add up to 180°

An exterior angle of a triangle is formed when any side is extended outwards.

How to find a missing angle outside of a triangle?

How to define the interior and exterior angles of a triangle and then state several theorems involving the interior and exterior angles of a triangle

The exterior angles of a triangle are the angles that form a linear pair with the interior angles by extending the sides of a triangle.

The sum of the exterior angles of a triangle and any polygon is 360 degrees.

The remote angles are the two angles in a triangle that are not adjacent angles to a specific exterior angle.

The sum of the remote interior angles is equal to the non-adjacent exterior angle.

### Sum Of Exterior Angles Of A Triangle

Two column proof of the sum of the exterior angles of a triangle is 360 degrees.

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