[Video] Q32: The points in the figure shown lie in the same plane. if triangle abf is congruent to triangle edg, where angle a corresponds to angle e and angle b corresponds to angle d, what is the measure, in degrees, of angle gcf? (disregard the degree symbol when gridding your answer.)

Explanation for Question 32 From the Math (Calc) Section on the 2020 October Sat

So question number 32 is asking us, what is the angle of GCF, 2 which is this angle right here. And not in order to find out that 3 angle, we need to know what this angle is in the triangle, 4 because then we can do 180 minus this 40 here, 5 minus whatever that angle is. And we'll get angle GCF, 6 cause all three should add up to 180. 7 Now, the way we find this mystery angle is by knowing that all of 8 these are not all of them, but all two of these triangles are congruent. 9 Triangles are congruent, then they have the same angle measures, 10 right? So since this triangle, 11 a B F has an angle of 40 and that 12 corner, then this mirror triangle that's congruent, 13 D G E is also going to have an angle of 40, 14 right? So these are the same one, just kind of mirrored and they're congruent. 15 So they have the same angle measures. If both of these are 40, 16 then I'm doing 180 minus 40 minus 40 or 180 17 minus 80. And that gives me an angle measure of a hundred degrees, 18 C.