In triangle ABC above, if ∠BAD and ∠ADB have measures of 4n°, ∠ACB ha

Question

https://gmatclub.com/forum/download/file.php?id=31213 In triangle ABC above, if ∠BAD and ∠ADB have measures of 4n°, ∠ACB has a measure of n°, and ∠DBC has a measure of 45°, what is the measure of ∠ABC? (Figure not necessarily drawn to scale.) A. 45° B. 60° C. 90° D. 105° E. 120° 2016-08-01_1649.png

Kurtosis · Answer

BAD = 4n
ADB = 4n
BDC = 180 - 4n
ACB = n
DBC = 45

BDC + ACB + DBC = 180
180 - 4n + n + 45 = 180
45 = 3n
n = 15

ABD = 180 - (BAD + ADB) = 180 - 120 = 60

ABC = 60 + 45 = 105

Answer: D

garcmillan · Answer

Hi all,

I think this is not an overly complicated geometric question as the only general rule that we need to know is that the sum of all angles of a triangle must be 180º, and that the angles over a line is also 180º. Everything is explained and calculated in the below image

ANSWER D

bumpbot · Answer

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In triangle ABC above, if ∠BAD and ∠ADB have measures of 4n°, ∠ACB ha

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GMAT Problem Solving (PS) Questions

In triangle ABC above, if ∠BAD and ∠ADB have measures of 4n°, ∠ACB ha

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