[Video] Q11: In the figure above, lines k, l , and m intersect at a point. if x + y = u +w. whihc of the following must be true? be true? i. x = z ii. y = w iii. z = t

Explanation for Question 11 From the Math (No Calc) Section on the Official Sat Practice Test 3

So in number 11, we're given a picture of some lines intersecting and were 2 given some information about the angles, right. 3 We're told the X plus Y so right here, 4 those two angles added together is equal to you. 5 Plus w these two angles add it together. 6 And so we're just going to go through each statement. We're going to see 7 if it's true. Right. And the important thing is that it must be true. 8 So it should always be true. Um, or if it could be true sometimes, 9 or if it's never true. And so we'll start with one X is equal 10 to Z, right? So we're thinking about this angle right here, 11 being equal to this angle right here. And the first thing that we should 12 notice, right, is that why? 13 And do you, I'm going to race this for a second. Why and you 14 are what we call vertical angles, right? 15 So they're equal to each other. Y is equal to you. 16 And then if we look at, well, I guess from there, 17 that means that X, Y X, 18 Y, X plus w would also be equal to Z plus T those two 19 must be the same, because those two are also like vertical angles. 20 Right? And if we notice what line M is doing, 21 Y and M cuts straight through those two angles, 22 it cuts them in half, right? So if these two angles right here, 23 if this is the same as this one, and then they're both being cut 24 in half, but that means that X and Z must also be the same, 25 because they're both half of that angle. So one is in fact true, 26 and we can eliminate answer choice C. Now, 27 if we ...