# Question Video: Finding Unknown Angles in Problems Involving Parallel Lines

Answer the questions for the given figure. Find the values of đť‘Ą and đť‘¦.

02:25

### Video Transcript

Answer the questions for the given figure.

Itâ€™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 đť‘Ą and đť‘¦.

First looking at đť‘Ą, đť‘Ą 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 đť‘Ą plus 60 equal to 180 and then subtract 60 and find that đť‘Ą is equal to 120. So đť‘Ą is equal to 120 degrees.

Now we need to solve for đť‘¦. Angle đť‘¦ and the angle thatâ€™s not labelled would be considered same side interior angles, just as we had before. So the angle that we donâ€™t have we need to solve for, which we will be able to do because the unknown angle â€” letâ€™s just call it đť‘§ â€” and the 110 degrees should add to be 180 because they make a straight line. So đť‘§ plus 110 equals 180. And we solve for đť‘§ by subtracting 110 from both sides of the equation. So đť‘§ is equal to 70.

Therefore, this angle is 70 degrees. So the same side interior angles of đť‘¦ and 70 add to be 180. And we solve for đť‘¦ the same as weâ€™ve been doing by subtracting 70 from both sides of the equation. And we get that đť‘¦ is equal to 110. So we can plug that in.

Now notice both of the pink angles are 110. Theyâ€™re equal. And the reason why theyâ€™re equal is because these are corresponding angles. And corresponding angles are equal.

So before wrapping up, we may be wondering, â€śWhy donâ€™t these add to 180 like the others?â€ť Thatâ€™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 đť‘Ą is equal to 120 degrees and đť‘¦ is equal to 110 degrees.