Exterior Angles Of A Triangle - Online Math Learning

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°

Exterior Angle of a Triangle An exterior angle of a triangle is formed when one side of the triangle is extended beyond its vertex. It is the angle between the extended side and the adjacent side of the triangle.

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

Geometry Worksheets Exterior Angle Worksheets Printable & Online Geometry Worksheets

Properties:

1. Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles (also called remote interior angles).
2. Sum of Exterior Angles: The sum of the measures of the exterior angles of any triangle (one at each vertex) is always 360 degrees.
3. Relationship with Interior Angles: At each vertex, the exterior angle and the interior angle are supplementary (they add up to 180°)

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.

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How to find a missing angle outside of a triangle?

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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.

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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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