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GMAT: Math 48

226, pg. 183. Created by Sal Khan.

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Video transcript

We're on problem 226. In the figure above-- let me draw the figure above. So I have a line there, then I have another line that's like that, and then this is a triangle like that, and then they draw another line that goes straight down like that. And they call this right here z degrees, this is y degrees, this is x degrees. They tell us that these are right angles. Fair enough. In the figure above, if z is equal to 50, so that is equal to 50 degreeS, then x plus y is equal to what? Well if z is 50-- well, first of all, we know since these are both right angles, both of these lines are going to be parallel, right? Both of those lines are parallel. And so you can view this green line as a transversal of the parallel. And so, z and y are corresponding angles, so y is also going to be 50. That should make a little intuitive sense, but you could watch the Khan Academy geometry videos if that doesn't make sense. But just eyeballing it looks right, too, but that's a property of transversals and parallel lines. And if that's true, then what is this angle right here? Well, 50 plus 90 plus this angle is equal to 180, right? So we could say 50 plus 90 plus theta is equal to 180. So you get 140 plus theta is equal to 180. Subtract 140 from both sides, so theta is equal to 40 degrees. So this angle right here is 40 degrees. What's x? Well, they're supplementary. They have to add up. They have to add up to be 180, right? This whole angle's 180. So that whole angle is 180, this is 40, then x has to be 140 degrees. So they wanted to know what x plus y is? Well x is 140, y is 50, so 140 plus 50 is 190 degrees. And that is not one of the choices. So I must have -- oh, I see my mistake. This angle right here, actually, we're still completely fine. This angle right here isn't y. This angle right here is y. But everything we did so far still holds. If this angle is 50, this angle is still 50 since it's a corresponding angle, right? And if that's 50, this is 90, then this is 40, x is 140. Now we just have to figure out what y is. Well, y is supplementary with this angle right here, right? So y plus this angle that I used to think was y until I looked closely at the drawing, y plus 50 has to be equal to 180 degrees, right? Because it's complementary with this 50 degree angle. So y is equal to 130. So x plus y is equal to 140 plus 130, which is equal to 270 degrees, and that's choice D. Problem 227. Looks like they've drawn another coordinate axis, which I'll draw. Nope, that's not what I want to draw with. I'll draw with that. OK, and then they have a line that comes down something like that. And they mark it off. They say that this is-- let me see how they mark it off. They say that this is the point 1, this is the point 2. They don't write the 2 there. They call this line l. This is the origin. This is the x-axis and that is the y-axis. And they say in the coordinate system above, which of the following is the equation of line l? Well, if we just eyeball it-- I mean, they don't say it explicitly, but it looks like this is intersecting at y is equal to 2, and this is intersecting at y is equal to 3. I guess that's a safe assumption. So how do we set up this equation? Well, you just have to figure out the slope of the y-intercept. We already know the y-intercept, right? It intersects-- when x is 0-- so y of 0. When x is 0, y is equal to 2, so that's the y-intercept, and now we just have to figure out the slope. Well, let's think about the slope. If we take this point-- well, I'll do it the formal way, right? The slope is equal to change in y over change in x. So let's take this as the end point. This is 3 comma 0, [PHONE RINGS] and let's see who's on the phone. If it's someone-- oh, I'll take that call. I'll continue this in the next video.