Explanation for Question 7 From the Math (Calc) Section on the Official Sat Practice Test 9
Question seven provides us with this figure and it asks us 2 in the figure above line, Ady intersects B E at C if 3 X is equal to 100, what is the value of Y? 4 Okay. So let's go through the information that we have. 5 We know that line a D this one right here, 6 intersects line bee. This one right here at, 7 see this point right here. 8 So it's already drawn in the picture and we know that X is equal 9 to 100, so that angle is equal to 100 degrees. 10 And we're trying to find the value of Y. 11 So because these two angles are 12 straight across from each other due to this intersection, 13 we know that they will be the same. So the measurement of angle BCA 14 is going to be equal to the measurement of angle DCE. 15 And we can actually find the measurement of angle BCA from the knowledge 16 that all angles in a triangle. 17 So it's 180 degrees, and we know the measurements of angle B and angle 18 a so 180 is equal to 20 degrees plus 19 a hundred degrees plus angle 20 that's angle BCA, excuse me. So, plus let's just call that X 180 21 is equal to 120 plus X. 22 We've got that. X is equal to 60 degrees. 23 So we know that that angle right here is equal to 60 degrees as 24 is that angle angle DCE. 25 Now let's draw a triangle C D E to visualize what's going on here. 26 We know that this angle is 60 degrees and the single is 40 degrees. 27 And now we can solve for Y CDE, 28 because again, we know that the angles altogether should add up to 180. 29 So we have 180 is equal to 60 plus 40 plus 30 Y. So we have a hundred plus Y is equal to 180. 31 I'm gonna get Y is equal to 80 degrees. 32 So we can pick C as our answer to.