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29 Aug 2016, 03:59
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Difficulty:
55%
(hard)
Question Stats:
60% (02:12) correct
40%
(02:16)
wrong
based on 81
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Not Attempted Yet
In triangle ABC above, if ∠BAD and ∠ADB have measures of 2n°, and if ∠ACB has a measure of n°, what is the length of side AB? (Figure not necessarily drawn to scale.)
(1) n = 25°
(2) CD = 4
Attachment:
2016-08-29_1458.png [ 3.8 KiB | Viewed 2773 times ]
Senthil1981
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29 Aug 2016, 12:21
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Bunuel
Based on the figure and Question stem :
∠BAD = ∠ADB = 2n° which means ∠ABD = 180 - 4n° and AB = BD
∠ACB = n° and ∠BDC = 180 - 2n° and hence ∠DBC = n° and BD = CD
What is AB ?
Now consider 1) n = 25° , Not sufficient, since only one angle is given. Eliminate A and D
Consider 2) CD = 4 , We've derived based on the stem that AB = BD = CD = 4,
Hence 2 is sufficient.
Hence B
29 Aug 2016, 14:37
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Bunuel
In triangle ABC, Angle BDN = 180-2n
Angle DBN= 180 -(180-2n) -n = n
or, BD=DC (sides opposite equal angles)
or, AB=BD=DC
From Statement 1: No data on the length of the side. Not sufficient
From Statement 2: CD = 4 = AB
Answer B
