Official Guide Explanation:
Problem Solving #48

Background

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Solution and Metadata

Question: 48
Page: 159
Difficulty: 4 (Moderately Easy)
Category 1: Geometry > Lines >
Category 2: Geometry > Triangles > other

Explanation: Given that AB and CE are parallel, we can assign variables to several more angles. For instance, angle DCE is x and angle EAB is y. We know that y = 45, so we can plug that in in both places.

Since CE = DE, the triangle on the right is isoceles. Since DCE is x, CDE must be x as well. The three angles in triangle CDE, then, are x, x, and 45. Since those angles must sum to 180, we can solve for x:

180 = x + x + 45

2x = 135

x = 67.5, choice (C).

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