Explanation for Question 18 From the Math (No Calc) Section on the Official Sat Practice Test 3
Now a number 18 were given to triangles, 2 right? And we're told that they're isosceles triangles, 3 which is why we can see that each triangle has a pair of congruent 4 sides. And then we're told that 180 minus Z is equal to two Y 5 and Y is equal to 75. And then we want to know the value 6 of X. Right? And so it's important to start thinking kind of working backwards 7 here. Right? We see the X is on a straight line with what we'll 8 call a right. So if I can find angle a, 9 then I'll be able to find out X and I can use angle Z 10 to find angle a. Um, 11 and so I'll start here, right? We're told that Y is 75. 12 So I can take this equation from the top, 13 right. Uh, right here. But instead of writing, Y I'll write 75 and 14 that'll allow me to solve for Z, 15 which will help me find a, so if that 180 minus Z is equal 16 to two times 75, which is one 50. 17 Now I'll subtract 180 from both sides so that I can get rid of 18 this 180. It'll cancel, I'll get the negative. 19 Z is equal to negative 30, and now I have a negative Z, 20 right? So I'll just divide both sides by negative one. 21 Um, that way I can cancel out this negative and I get the Z 22 is equal to 30, right? So Z is 30. 23 And what's important to know here is that since both of these sides are 24 the same, both of these other angles are also the same, 25 right? So I really have two angles that we could call angle a, 26 so essentially a plus a plus a plus a plus 30 is 27 equal to 180, because those are all my ang...