Bunuel wrote:
What is a in terms of b and y?
(A) b + y + 65
(B) b – y + 65
(C) b + y + 75
(D) b – 2y + 45
(E) b – y + 75
Attachment:
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Since a is an exterior angle of the triangle on the left, a = x + 90 or x = a - 90
Since b is an exterior angle of the triangle on the right, b = x + 10 + y + 5 or b = x + y + 15.
Now we can substitute x = a - 90 into b = x + y + 15:
b = a - 90 + y + 15
a + y - 75 = b
a = b - y + 75
Alternate Solution:
Since a and y are supplementary angles, a + y = 180 or a = 180 - y.
Since b is an exterior angle of the triangle on the right, b = x + 10 + y + 5 or b = x + y + 15.
Since x + y + 90 = 180, x + y = 90. Substituting this for the expression for b, we get b = 90 + 15 = 105.
Then, a = 180 - y = 105 + 75 - a = b + 75 - y.
Answer: E
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