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by Max@Math Revolution » Fri Mar 13, 2020 1:47 am
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[GMAT math practice question]

We have \(\triangle ABC\) with ∠BAC = 50. BD and CD bisect equally ∠B and ∠C, respectively, as the figure shows. What is the measure of ∠BDC?
3.9ps.png
A. 55
B. 60
C. 65
D. 70
E. 75
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Re: We have

by Max@Math Revolution » Mon Mar 16, 2020 2:57 am
=>
3.9ps(a).png
We have b + c + 50 = 180 or b + c = 130
We also have 2x + b = 180 and 2y + c = 180.
When we add those equations, we get
2x + b + 2y + c = 180 + 180
2x + 2y + b + c = 360 (adding like terms)
2(x + y) + b + c = 360 (factoring out a common factor of 2)
2(x + y) + (b + c) = 360 (grouping terms)
2(x + y) + 130 = 360 (substituting 130 = b+ c from above)
2x + 2y + 130 = 360 (multiplying 2 through the bracket)
2x + 2y = 230 (subtracting 130 from both sides)
x + y = 115 (dividing both sides by 2)

Thus ∠BDC = 180 – (x + y) = 180 - 115 = 65.

Therefore, C is the answer.
Answer: C
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