GRE Math Challenge Question #27 : What is the value of x + y?
In the triangle shown above, AB is parallel to CE. What is the value of x + y?
A. 50
B. 90
C. 140
D. 175
E. 190
Explanation:
Redraw the figure, labeling all information given:
Since BA and CE are parallel, angle B and minor angle C are equivalent, as shown:
The two angles that meet at C make up a straight line, so they sum to 180 degrees:
180 = y + 40
y = 140
The three angles of triangle CDE must sum to 180 degrees, and so
180 = 40 + 90 + x
180 = 130 + x
x = 50
Therefore, x + y = 140 + 50 = 190.
Correct Choice: (E) 190
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