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In the figure below, point I is the incenter of △ABC and line AH is perpendicular to BC. If ∠ABC = 80 and ∠ACB = 50 w

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In the figure below, point I is the incenter of △ABC and line AH is perpendicular to BC. If ∠ABC = 80 and ∠ACB = 50 w

by Max@Math Revolution » Tue Feb 04, 2020 1:23 am
[GMAT math practice question]

In the figure below, point I is the incenter of △ABC and line AH is perpendicular to BC. If ∠ABC = 80 and ∠ACB = 50 what is ∠x + ∠y?
2.4PS.png
A. 55
B. 60
C. 65
D. 75
E. 80
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Re: In the figure below, point I is the incenter of △ABC and line AH is perpendicular to BC. If ∠ABC = 80 and ∠ACB = 50

by Max@Math Revolution » Wed Feb 05, 2020 11:40 pm
=>

∠BAC = 180 – 80 – 50 = 50.
An incenter of a triangle is the intersection of lines bisecting all interior angles.
∠x = ∠CAH - ∠CAI = 40 – 25 = 15.
∠y = ∠CAI + ∠ACI = 25 + 25 = 50.
Thus ∠x + ∠y = 15 + 50 = 65.

Therefore, C is the answer.
Answer: C
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