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In the figure, what is ∠ a + ∠ b + ∠ c + ∠ d + ∠ e

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by Max@Math Revolution » Mon Oct 21, 2019 12:33 am
[GMAT math practice question]

In the figure, what is ∠ a + ∠ b + ∠ c + ∠ d + ∠ e - ∠ f + ∠ g?

A. 270
B. 300
C. 330
D. 360
E. 420

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by Max@Math Revolution » Tue Oct 22, 2019 11:59 pm
=>

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We have < a + < b + 180° - <x = 180°.
< c + < d + < e + < y = 360°
< g + < z + < x = 180°
< f + < y + < z = 180°
When we add the first three equations and subtract the last equation, we have
< a + < b + 180° - < x + < c + < d + < e + < y + < g + < z + < x - (< f + < y + < z) = 180° + 360° + 180° - 180°
=>< a + < b + < c + < d + < e - < f + < g + 180°= 540°
=>< a + < b + < c + < d + < e - < f + < g = 360°

Therefore, D is the answer.
Answer: D
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