In this video, Achievable GRE course author Matt Roy shows you how to solve a tricky angles problem where very little information is given. He uses multiple angle and triangle rules to determine the values of the unknown angles.
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00:00:02 Here we have a geometry question that looks kind of complicated. There's many lines, a couple triangles and a lot of unknown angles. Quantity A is X or the value of angle X and quantity B is half of Y. So we don't really have much information here. We only know that one angle is at 90 degrees and another angle is at 148. 00:00:29 So with questions like these, we need to start filling in what we can solve for 1st, and later determine if that gives us enough information to solve for what we're looking for. So let's just start from the 148 angle. 148 is on the same line as the next angle, so they must sum up to 180 degrees. 00:00:57 So we take 148 + X = 180, subtract 148 from both sides and you get X = 32. And we also know that opposite angles must equal, so that angle opposite X which is 32 should also be 32. Now now you may notice that we have a little triangle there where two of the three angles are known. 00:01:25 90 degrees, 32 degrees, and unknown angle. We can sum all of these up to 180, so 90 + 32 + X = 180 and solve for X. After subtracting 90 and 32 from both sides, we should get 58 for that angle. Again, opposite angles are equal, so we put a 58 on the opposite side of that angle there and yet. 00:01:54 Again, we have another triangle with two known angles and one unknown angle. That's because we've already solved for X, so we can fill in that angle for X. We can put 32 there, and now 32 + 58 + X, which is that bottom right angle that we don't know yet, equals 180 degrees. Subtract 32 and 58 from both sides and you'll get 90 for that angle. 00:02:24 And because that angle and the Y angle rest on the same line again, those have to add up to 180 degrees. Well 90 + 90 is 180, so Y must be 90. Considering that quantity B is half of Y or half of 90, we can say quantity B is 45 and quantity A X we already know to be 32, so. 00:02:53 Quantity B must be greater than Quantity A.