Official Guide Explanation:
Problem Solving #209




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Solution and Metadata

Question: 209
Page: 182
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Triangles > Multiple figures
Category 2: Geometry > Intersecting Lines and Angles >

Explanation: The angles in a quadrilateral sum to 360, so 90 + 90 + z + y = 360, or y = 180 - z. The angles in a triangle sum to 180, so the angle opposite x\unit{%TCIMACRO{\U{b0}}%BeginExpansion {{}^ ο}%EndExpansion } is equivalent to 180 - 90 - z = 90 - z. Since 90 - z and x make up a straight line, they sum to 180, so 180 = 90 - z + x, or x = 90 + z. Putting all of that together, x + y = (90 + z) + (180 - z) = 270, choice (D).

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