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

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Math Expert
Joined: 02 Sep 2009
Posts: 49272
Given rectangle ABCD, what is the value of angle DEC?  [#permalink]

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03 Jul 2018, 10:53
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Difficulty:

45% (medium)

Question Stats:

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

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

(2) CE/BE = 2

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Math Expert
Joined: 02 Aug 2009
Posts: 6792
Re: Given rectangle ABCD, what is the value of angle DEC?  [#permalink]

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03 Jul 2018, 13:34
Bunuel wrote:

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

(2) CE/BE = 2

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

See the attached figure

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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03 Jul 2018, 13:43
Bunuel wrote:

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

(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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