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The figure shows that ∠ ABF=∠ ACF=∠ FEC=30 and DE is p

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The figure shows that ∠ ABF=∠ ACF=∠ FEC=30 and DE is p

by Max@Math Revolution » Thu Oct 10, 2019 11:42 pm
[GMAT math practice question]

The figure shows that ∠ ABF=∠ ACF=∠ FEC=30 and DE is parallel to the BC. What is the measure of ∠ DEF?

Image

A. 110
B. 120
C. 130
D. 140
E. 150
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by Max@Math Revolution » Sun Oct 13, 2019 5:10 pm
=>

Since DE and BC are parallel and < BFE and< DEF are same side interior angles, we have < DEF + < BFE = 180 .
Since < BFE is an exterior angle and it equals to the sum of the non-adjacent interior angles, < FEC + < ACF = 30 + 30 = 60 .
So, we have < DEF = 180 - < BFE = 180 - 60 = 120.

Therefore, B is the answer.
Answer: B
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