Official Guide Explanation:
Data Sufficiency #132




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Solution and Metadata

Question: 132
Page: 284
Difficulty: 5 (Moderate)
Category 1: Geometry > Intersecting Lines and Angles >
Category 2: Geometry > Quadrilaterals >

Explanation: Note that all four of the named angles are adjacent to interior angles of a quadrilateral. The angle to the right of x is 180 - x , the angle to the left of y is 180 - y, and so on. The interior angles of a quadrilateral always sum to 360, so we can set up an equation:

(180 - x) + (180 - y) + (180 - w) + (180 - z) = 360

720 - x - y - w - z = 360

360 = x + y + w + z

Since we're looking for x + y, we need the values of w and z.

Statements (1) and (2) are both insufficient on their own. They give us one of the two angles we need, but not both. Don't fall in the trap of assuming that any of the lines are parallel--not only do they not appear parallel, but also, in general, Data Sufficiency diagrams are unreliable.

Taken together, the statements are sufficient. If w = 95 and z = 125, we can solve for x + y:

360 = x + y + w + z

360 = x + y + 95 + 125

x + y = 140

Choice (C) is correct.

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