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