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The figure shows that l is parallel to m and ∠ABC=60o, ∠

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The figure shows that l is parallel to m and ∠ABC=60o, ∠

by Max@Math Revolution » Thu Oct 17, 2019 4:54 pm
[GMAT math practice question]

The figure shows that l is parallel to m and ∠ ABC=60, ∠ BCD=30, and ∠ CDE=90. What is the measure of ∠ DEF?

A. 100
B. 110
C. 120
D. 130
E. 140

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by Max@Math Revolution » Sun Oct 20, 2019 5:50 pm
=>

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We draw lines p and q parallel to l and m.
When we put < DEF = < DHI = < x and < GDC=< y, we have < HDJ=< DHC=180°-x
Since we have < ABG=< GCD and < GDC=< DCH, we have 60°=30°+< y and < y=30°.
Since < GDC+< CDH+< HDJ=180° or < y+90°+180°-< x=180°, we have 30°+270°-< x=180°, 300°-< x=180° or < x = < DEF = 120°.

Therefore, C is the answer.
Answer: C
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