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# GMAT: MathÂ 48

## 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.