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## Official Guide Explanation:Problem Solving #48

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

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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