WEBVTT
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Answer the questions for the given figure.
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It’s important to note these arrows.
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This means that these lines are parallel.
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And if these lines are parallel, these lines are called transversals.
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And we can use properties to help solve for 𝑥 and 𝑦.
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First looking at 𝑥, 𝑥 degrees and a 60-degree angle are considered same side interior angles.
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And they add to 180 degrees.
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So if we know that one of them is 60, we can set 𝑥 plus 60 equal to 180 and then subtract 60 and find that 𝑥 is equal to 120.
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So 𝑥 is equal to 120 degrees.
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Now we need to solve for 𝑦.
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Angle 𝑦 and the angle that’s not labelled would be considered same side interior angles, just as we had before.
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So the angle that we don’t have we need to solve for, which we will be able to do because the unknown angle — let’s just call it 𝑧 — and the 110 degrees should add to be 180 because they make a straight line.
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So 𝑧 plus 110 equals 180.
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And we solve for 𝑧 by subtracting 110 from both sides of the equation.
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So 𝑧 is equal to 70.
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Therefore, this angle is 70 degrees.
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So the same side interior angles of 𝑦 and 70 add to be 180.
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And we solve for 𝑦 the same as we’ve been doing by subtracting 70 from both sides of the equation.
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And we get that 𝑦 is equal to 110.
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So we can plug that in.
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Now notice both of the pink angles are 110.
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They’re equal.
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And the reason why they’re equal is because these are corresponding angles.
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And corresponding angles are equal.
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So before wrapping up, we may be wondering, “Why don’t these add to 180 like the others?”
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That’s because, in order to be same side interior angles, it has to be one transversal through a pair of parallel lines.
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And these two angles only intersect one of their parallel lines.
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So this does not work for same side interior.
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So again, our answers would be that 𝑥 is equal to 120 degrees and 𝑦 is equal to 110 degrees.