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Given rectangle ABCD, what is the value of angle DEC?

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Given rectangle ABCD, what is the value of angle DEC?  [#permalink]

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New post 03 Jul 2018, 10:53
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

77% (01:45) correct 23% (01:20) wrong based on 30 sessions

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Re: Given rectangle ABCD, what is the value of angle DEC?  [#permalink]

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New post 03 Jul 2018, 13:34
Bunuel wrote:
Image

Given rectangle ABCD, what is the value of angle DEC?


(1) AD = AE

(2) CE/BE = 2


Attachment:
The attachment Untitled+.png is no longer available



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
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Re: Given rectangle ABCD, what is the value of angle DEC?  [#permalink]

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New post 03 Jul 2018, 13:43
Bunuel wrote:
Image

Given rectangle ABCD, what is the value of angle DEC?


(1) AD = AE

(2) CE/BE = 2


Attachment:
Untitled+.png


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
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Re: Given rectangle ABCD, what is the value of angle DEC? &nbs [#permalink] 03 Jul 2018, 13:43
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