The figure shows that AB is parallel to FE. What is ∠ABC

[Max@Math Revolution]

[GMAT math practice question]

The figure shows that AB is parallel to FE. What is ∠ ABC + ∠ BCD + ∠ CDE + ∠ DEF?



A. 380
B. 440
C. 540
D. 600
E. 720

[Max@Math Revolution]

Draw two lines GK and HO parallel to AB and FE as follows.



Then we have ∠ ABC + ∠ BCG = 180°, ∠ GCD + ∠ CDH = 180°, ∠ HDE + ∠ DEF = 180°, and the pairs of two angles are supplementary, respectively.
∠ ABC + ∠ BCD + ∠ CDE + ∠ DEF = ∠ ABC + (∠ BCG + ∠ GCD) + (∠ CDH + ∠ HDE) + ∠ DEF = (∠ ABC + ∠ BCG) + (∠ GCD + ∠ CDH) + (∠ HDE + ∠ DEF) = 180° + 180° + 180° = 540°,

Therefore, C is the answer.
Answer: C