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In the figure shown what is the measure of angle x

In the figure shown what is the measure of angle x-example-1
User Kayahr
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1 Answer

3 votes

Answer:

115°

Explanation:

You want to know the measure of exterior angle x, which is opposite remote interior angles measuring 65° and 50°.

Exterior angle theorem

The measure of the exterior angle (x) is the sum of the remote interior angles:

x = 65° +50° = 115°

The measure of angle x is 115°.

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Additional comment

The sum of the two marked interior angles is the supplement of the unmarked interior angle. That is, the three angles together total 180°.

The exterior angle x is the supplement of the unmarked interior angle. Together, they are a linear pair, so total 180°.

Two angles supplementary to the same angle have the same measure. That is, (65° +50°) and x are both supplementary to the unmarked interior angle, so are equal. x=65°+50° = 115°. The above theorem is a summary of this relationship.

User Roger Gustavsson
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