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17 Jul 2017, 23:31
Kudos
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
59% (02:37) correct
41%
(02:54)
wrong
based on 102
sessions
History
Date
Time
Result
Not Attempted Yet
In the diagram below, triangle ABC is right-angled at B. What is the measure of ∠BAC?
(1) BD = BC and AE = AD.
(2) BE = DE.
2017-07-18_1030.png [ 6.99 KiB | Viewed 4760 times ]
(1) BD = BC and AE = AD.
(2) BE = DE.
Attachment:
2017-07-18_1030.png [ 6.99 KiB | Viewed 4760 times ]
18 Jul 2017, 05:03
Kudos
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i have tried every possible thing to get the answer but knowing that two sides are same, i cant get the angle of the other side. I cant find the relationship between the two small triangles even...so E for me
18 Jul 2017, 05:36
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Bunuel
It should be C
Statement 1: Insufficient
(1) BD = BC and AE = AD.
This tells us both top and bottom triangles are isosceles but it does not provide us any information about the central triangle.
Statement 2: Insufficient
This tells us central triangle is an isosceles but it does not give out information about the angles.
Lets combined 1 and 2.
From 1, Since \(BD = BC\), we know \(∠BDC = ∠BCD\). Let us call this angle x. In the triangle \(BDC\), third angle \(∠CBD\) would be equal to \(180 - 2x\).
Since triangle ABC is right angled at B, \(∠EBD = 90 - (180 - 2x) = -90 + 2x\)
From 2, we know \(BE = DE\), hence \(∠EBD = ∠EDB = -90 + 2x\)
The third angle in the central triangle would be \(180 - 2 (-90 + 2x) = 360 - 4x\)
Lets name the two equal angles from triangle \(AED = y\)
At point D, we have
\(x + (-90 + 2x) + y = 180\)
\(3x + y = 270\) --- (1)
At point E, we have
\(360 - 4x + y = 180\)
\(4x - y = 180\) --- (2)
Solving the two equations, we get the value of y and since two angles in triangle AED are y, the third \(∠BAC\) can be calculated using \(180 - 2y\).
Edit: resizing diagram as it was too large.
Attachments
diagram.jpg [ 28.2 KiB | Viewed 4209 times ]
