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In triangle ABC above, if ∠BAD and ∠ADB have measures of 4n°, ∠ACB ha
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Bunuel
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In triangle ABC above, if ∠BAD and ∠ADB have measures of 4n°, ∠ACB ha [#permalink] New post  01 Aug 2016, 04:51
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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°

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Kurtosis
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Re: In triangle ABC above, if ∠BAD and ∠ADB have measures of 4n°, ∠ACB ha [#permalink] New post  01 Aug 2016, 05:01
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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
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In triangle ABC above, if ∠BAD and ∠ADB have measures of 4n°, ∠ACB ha [#permalink] New post  16 Aug 2020, 13:06
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
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