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What is the Exterior Angle Theorem?

Back

The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

Tags

CCSS.8.G.A.5

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What are remote interior angles?

Back

Remote interior angles are the two angles inside a triangle that are not adjacent to a given exterior angle.

Tags

CCSS.8.G.A.5

Front

If Angle W is an exterior angle, which angles are its remote interior angles?

Back

The remote interior angles to Angle W are the two angles inside the triangle that do not share a vertex with Angle W.

Tags

CCSS.8.G.A.5

Front

How do you find the measure of an exterior angle?

Back

To find the measure of an exterior angle, add the measures of the two remote interior angles.

Tags

CCSS.8.G.A.5

Front

If Angle X = 50° and Angle Y = 70°, what is the measure of the exterior angle formed at their vertex?

Back

The measure of the exterior angle is 50° + 70° = 120°.

Tags

CCSS.8.G.A.5

Front

What equation can be set up to find an unknown angle x in a triangle using the Exterior Angle Theorem?

Back

The equation can be set up as: exterior angle = remote interior angle 1 + remote interior angle 2.

Tags

CCSS.8.G.A.5

Front

If Angle A is 40° and Angle B is 60°, what is the measure of the exterior angle at Angle A?

Back

The measure of the exterior angle at Angle A is 40° + 60° = 100°.

Tags

CCSS.8.G.A.5

Front

What is the relationship between an exterior angle and its adjacent interior angle?

Back

The exterior angle is equal to the sum of the two remote interior angles, while the adjacent interior angle is not included in this sum.

Tags

CCSS.8.G.A.5

Front

If the exterior angle is 130°, what are the possible measures of the remote interior angles?

Back

The sum of the remote interior angles must equal 130°; for example, 70° and 60°.

Tags

CCSS.8.G.A.5

Front

How can you verify the Exterior Angle Theorem using a triangle?

Back

By measuring the exterior angle and the two remote interior angles, and confirming that their sum equals the exterior angle.

Tags

CCSS.8.G.A.5