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# In the quadrilateral above, if AB = BD = BC, and AD = CD, then x =

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Math Expert
Joined: 02 Sep 2009
Posts: 47983
In the quadrilateral above, if AB = BD = BC, and AD = CD, then x =  [#permalink]

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12 Nov 2017, 10:21
3
2
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(N/A)

Question Stats:

48% (01:32) correct 52% (01:07) wrong based on 27 sessions

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In the quadrilateral above, if AB = BD = BC, and AD = CD, then x =

(A) 70
(B) 60
(C) 50
(D) 40
(E) 30

Attachment:

2017-11-12_2103.png [ 15.14 KiB | Viewed 873 times ]

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Math Expert
Joined: 02 Aug 2009
Posts: 6549
Re: In the quadrilateral above, if AB = BD = BC, and AD = CD, then x =  [#permalink]

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13 Nov 2017, 06:42
Bunuel wrote:

In the quadrilateral above, if AB = BD = BC, and AD = CD, then x =

(A) 70
(B) 60
(C) 50
(D) 40
(E) 30

Attachment:
The attachment 2017-11-12_2103.png is no longer available

No replies, so let me give it a try with a att figure

as C
Attachments

quad1.png [ 13.58 KiB | Viewed 547 times ]

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 24 Nov 2016
Posts: 152
Re: In the quadrilateral above, if AB = BD = BC, and AD = CD, then x =  [#permalink]

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13 Nov 2017, 07:41
Bunuel wrote:

In the quadrilateral above, if AB = BD = BC, and AD = CD, then x =

(A) 70
(B) 60
(C) 50
(D) 40
(E) 30

Attachment:
2017-11-12_2103.png

(1) Find angle ABC: if BD = BC, then BDC = BCD = 70 and DBC = 180 - 70(2) = 40. So, ABC = 40*2 = 80.
(2) Find angle ACD: if DA = DC, then ADC = 140 and ACD = (180 - 140) / 2 = 20.
(3) Find x: Triangle BCD or BAD = 180 = 70 + 40 + (x + 20), x = 50.
Intern
Joined: 09 Jun 2016
Posts: 15
Re: In the quadrilateral above, if AB = BD = BC, and AD = CD, then x =  [#permalink]

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13 Nov 2017, 10:35
Bunuel wrote:

In the quadrilateral above, if AB = BD = BC, and AD = CD, then x =

(A) 70
(B) 60
(C) 50
(D) 40
(E) 30

Attachment:
2017-11-12_2103.png

Hi Bunnel... as per quadrilateral rule the opposite angles need to be 180 degree but looking at the question and solving based on AAA concept the opposite angles of quadrilateral are going beyond 180 degree.. kindly help with your solution

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Re: In the quadrilateral above, if AB = BD = BC, and AD = CD, then x = &nbs [#permalink] 13 Nov 2017, 10:35
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