Question

Horizontal lines e and f are cut by vertical lines a and b. At the intersection of lines a and e, the uppercase right angle is (x + 1) degrees. At the intersection of lines a and f, the bottom right angle is (x minus 3) degrees. At the intersection of lines b and e, the bottom left angle is y degrees.
If a ∥ b and e ∥ f, what is the value of y?

87
88
91
92

Answer 1

92

Reason: Let the top-right angle at a∩e be x+1. Its vertical opposite (the bottom-left at a∩e) is also x+1. The bottom-right at a∩e is the supplement, 180 − (x+1) = 179 − x. Corresponding angles (since e ∥ f) make that equal to the top-right at a∩f, which is given as x − 3. So 179 − x = x − 3 → 2x = 182 → x = 91. Then y (the bottom-left at b∩e) equals the bottom-left at a∩e (since a ∥ b), so y = x + 1 = 92.