Explanation for Question 5 From the Math (No Calc) Section on the 2017 April Sat
Question five says in the figure above lines, 2 B, C and a D are parallel, 3 a B and a C are parallel, see D is equal to C E. 4 And the measure of ABC is 115 degrees. 5 What is the measure of angle BCD? 6 So the first thing we know is that ABC is equal to 115 7 degrees. And since we know that a or since we know that BC 8 and a D are parallel and that AB and ECR parallel, 9 we know that this angle angle AEC is also equal 10 to 115 degrees. So now that we know that we can find angle 11 D and to do that, we just have to do 180 minus one 15, 12 because these two angles are on a line and lines have a degree 13 of 180. And that gives me 65 14 degrees. So I know that this angle is equal to 65 degrees. 15 Next, I know that this angle over here is also equal to 65 degrees, 16 and that's because lines, CE and CD are the same length, 17 which means they're corresponding angles are the same degrees. 18 And finally, I can find angles. See, 19 and I can do that by doing 180, 20 the degree of a triangle minus 65 plus 21 65, 65 plus 65 is 130 and 22 180 minus 130 is 50. 23 So I know that this angle is 50 degrees, 24 but we're trying to find the angle degree of BCD, 25 which means we also have to find angle BCE and add that to ECD. 26 So we can do that by knowing that angles a and angle C are 27 the same degree, uh, 28 because of the parallel lines that I mentioned before. 29 So all we have to do is 360 degrees, 30 which is the total degrees of this, this, 31 uh, parallelogram minus 150 15 32 plus 115. And we need to divide that by two. 33 So 360 minus 115 plus 115, 34 well, 115 plus 115 is equal to two 30, 35 which means that 360 minus two 30 is one 30. 36 And that divided by two is 65, 37 which means that angle BCE is 65 degrees. 38 Finally, we just have to add 65 to 50 because we're looking for BCD, 39 which is this whole angle here. And 65 plus 40 50 is just equal to 115 degrees. 41 So we know that the correct answer is.