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I’m confused on what to do here. I’m supposed to find the angle measure for angles 1, 2, 3? And then explain my reasoning based off of the different types of theorems.

I’m confused on what to do here. I’m supposed to find the angle measure for angles-example-1
User Pratap Koritala
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1 Answer

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In the image, you have 3 parallel lines cut by a transversal and a given angle that measures 102° (let's call it 4).

The theorem of alternate exterior angles says that those angles are congruent. This means they have equal measures. Then, angle 2 is congruent to angle 4 as they are alternate exterior angles (they lie outside the two lines and on opposite sides of the transversal), then angle 2 measures 102°.

Alternate interior angles are those that lie between the two lines and on opposite sides of the transversal, then angle 4 and angle 1 are alternate interior angles, and the theorem says they are congruent, then angle 1 measures 102°.

Angles 2 and 3 are supplementary, which means they add up to 180°, then if angle 2 measures 102°, angle 3 measures 78° (180-102=78)

User Ahmed Tawila
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