Bunuel wrote:

Four lines intersect as shown in the figure above. If p = 50, what is the value of x + y?

(A) 230

(B) 240

(C) 260

(D) 270

(E) 300

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The right angles indicate that the two horizontal lines are parallel.

Angle p and the yellow-shaded angle are vertical angles, hence equal.

p = 50

yellow = 50

The yellow angle and the green angle are alternate interior angles of parallel lines cut by a transversal.

yellow = 50

green = 50

Finally, the green and blue angles are vertical angles and hence equal.

green = 50

blue = 50

Angles x, y, green, and blue surround a single point with 360 degrees.

green + blue = 100

x + y + green + blue = 360

x + y + 100 = 360

x + y = 360 - 100

x + y = 260

Answer C

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