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

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Math Expert
Joined: 02 Sep 2009
Posts: 60515

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01 Aug 2016, 05:51
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Difficulty:

55% (hard)

Question Stats:

62% (01:55) correct 38% (02:16) wrong based on 54 sessions

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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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Marshall & McDonough Moderator
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01 Aug 2016, 06:01
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

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