The figure shows the points A, B, C, … , G and

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Tue Jul 28, 2020 12:46 am

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[GMAT math practice question]

7.28PS.png

The figure shows the points A, B, C, … , G and $<$ B = 70°, $<$ C = 68°, $<$ D = 78°, $<$ E = 82°, $<$ F = 86° and $<$ G = 88°. What is $<$ A?

A.58°
B. 60°
C. 68°
D. 70°
E. 88°

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Source: Beat The GMAT — Problem Solving | Tue Jul 28, 2020 12:46 am

Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

Re: The figure shows the points A, B, C, … , G and

by Max@Math Revolution » Thu Jul 30, 2020 1:04 am

7.28ps(a).png

∠DBE + ∠CEB = ∠BDC + ∠ECD

The sum of all the interior angles of quadrilateral ACDF and triangle GBE is 360° + 180° = 540°.
The measure of the angle ∠A is
540° – ( 70° + 68° + 78° + 82° + 86° + 88° ) = 68°.

Therefore, the correct answer is C.
Answer: C

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