Alternate interior angles

0:00- [Narrator] We're told lines R and S are parallel and cut by a transversal T. So this is R and S. And we can see from these arrows that are pointing in the same direction that these are two parallel lines, they will never intersect. And a transversal is just a fancy word for another line that intersects both of those parallel lines.

0:20Now we're asked, which pairs of angles are alternate interior angles? Pause this video, have a go at that before we do it together. Okay, so when we're talking about alternate interior angles, we're talking about the scenario where you have a transversal intersecting two parallel lines.

0:39And if you think about the interior angles, those are the ones that you could say are between the two parallel lines. So for example, everything here that we're seeing is an interior angle. And then when we say alternate, we're really saying that they're alternating on either side of the transversal.

0:55So if we look at this angle right over here, that is, has a measure of X degrees and this angle right over here, these are alternate interior angles. So, and what we also know is that alternate interior angles are going to have the same measure. So not only are they the, not only are they alternate interior, but we also know that X degrees is going to be equal to Z degrees.

1:19Similarly, this angle and this angle they're on, they're both interior, but they're on opposite sides, or alternate sides I should say, of that transversal. This is on the right side, this is on the left side, at least the way it's oriented there. So this pair is also a pair of alternate interior angles.

1:36And we also know that Y degrees is equal to W degrees or that Y is going to be equal to W. Now let's use, let's use what we just talked about to actually calculate an angle. So here again, R and S are parallel, cut by a transversal, and we wanna figure out the value of X.

1:56Pause this video, have a go at that. Okay, so I, maybe I'm strange, but I really enjoy these questions where I have to figure out an angle based on some other information. And because there's many different ways to solve this puzzle, if you will. So one way to think about it is, all right, X, that we need to figure out, that right over there.

2:17That is an alternate interior angle with Z, right over here. So these are gonna have the same measure. So if we can figure out what Z is, then we know what X is and what's Z? Well, this Z degrees, plus this other angle here, the 65 degrees, they are supplementary.

2:38Notice when you add them together, you get all the way around. You go all the way around, that is 180 degrees. So we know that Z, I'll try to state true to these colors. Z plus 65, plus 65 is going to be equal to 180. Or if we wanna solve for Z, we just subtract 65 from both sides and we will get Z.

3:08Let me use that other color, we will get Z. These cancel out, is equal to 180 minus 65 is, let's see, that's gonna be 100. If I subtracted, that's 115. So Z right over here is equal to 115 degrees. Did I do that right? Yeah, if I had five, I get to 120 and then I add another 60, I get to 180.

3:34So that's 150 degrees and it's an alternate interior angle with X. So this is also 115 degrees and we're done. Now you said, "Hey, there's multiple ways of solving it, Sal" and yes indeed, there are multiple ways of solving it. You could have said that Y, because it is a vertical angle with a 65 degrees, that this is also going to be 65 degrees, and that's an alternative interior angle with W.

4:00So that's also 65 degrees and W and X are supplementary to each other, and you would've once again, gotten to 115 degrees. And that's not the only way to solve this. But I'll leave you there, two is enough for now.