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03 Jul 2018, 10:53
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C
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Difficulty:
25%
(medium)
Question Stats:
84% (01:59) correct
16%
(01:36)
wrong
based on 43
sessions
History
Date
Time
Result
Not Attempted Yet
Given rectangle ABCD, what is the value of angle DEC?
(1) AD = AE
(2) CE/BE = 2
Attachment:
Untitled+.png [ 9.46 KiB | Viewed 2114 times ]
03 Jul 2018, 13:34
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Bunuel
See the attached figure
1) AD = AE
So angle AED is 45
But nothing more
Insufficient
2) CE/BE=2
BCE is a right angled triangle and ratio of one side to hypotenuse is 1:2
So triangle is 30:60:90 and sides are in 1:√3:2..
So BEC =60
Nothing more
Insufficient
Combined
Angle DEC =180-45-60=75
Sufficient
C
Attachments
PicsArt_07-04-01.59.20.jpg [ 16.43 KiB | Viewed 1892 times ]
03 Jul 2018, 13:43
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Bunuel
Question stem:-\(\angle{DEC}\)=?
Statement 1:-
AD=DE implies that \(\angle{ADE}\)=\(\angle{AED}\)=\(45^{\circ}\)
No other info provided to calculate \(\angle{DEC}\).
hence, insufficient.
Statement 1:-
\(\frac{CE}{BE}\)= 2
Or, CE=2x, BE=x.
In the right angled \(\triangle\)CEB, BC=\(\sqrt{3}x\)
So, it is a \(30^{\circ}-60^{\circ}-90^{\circ}\) \(\triangle\).
So, \(\angle{BEC}\)=\(60^{\circ}\)
No other info provided to calculate \(\angle{DEC}\).
hence, insufficient.
(1)+(2), we have ,\(\angle{AED}+\angle{DEC}+\angle{BEC}=180^{\circ}\)
From st1, we know the measure of \(\angle{AED}\) & from st2, we know the measure of \(\angle{BEC}\); hence measure of \(\angle{DEC}\) can be definitely calculated.
Ans. C
