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The figure shows that triangle ABC is inscribed in circle O.

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by Max@Math Revolution » Mon Oct 28, 2019 12:16 am
[GMAT math practice question]

The figure shows that triangle ABC is inscribed in circle O. If ∠ AOB = x + 60, ∠ BOC = 2x + 20, ∠ AOC = 3x - 20, what is ∠ ACB?

A. 45
B. 50
C. 55
D. 60
E. 65

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by Max@Math Revolution » Tue Oct 29, 2019 11:19 pm
=>

Since the sum of central angles of those three sectors equals to 360°, we have x + 60°+ 2x + 20°+ 3x - 20°= 360°, 6x + 60°= 360°, 6x = 300°, or x = 50°
Then we have ∠ AOB = x + 60° = 50° + 60° = 110°, ∠ BOC = 2x + 20° = 2(50°) + 20° = 120°, ∠ AOC = 3x - 20° = 3(50°) - 20° = 130°.

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∠ ACO = (180°- 130°)/2 = 25° and ∠ BCO = (180°- 120°)/2 = 30°.
Then ∠ ACB = ∠ AOC + ∠ BOC = 25°+ 30°= 55°.

Therefore, C is the answer.
Answer: C
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