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# In the figure, ABCD is a parallelogram, what is the value of b ?

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Joined: 02 Sep 2009
Posts: 53066
In the figure, ABCD is a parallelogram, what is the value of b ?  [#permalink]

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09 Oct 2018, 22:37
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Difficulty:

15% (low)

Question Stats:

95% (01:05) correct 5% (00:58) wrong based on 28 sessions

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In the figure, ABCD is a parallelogram, what is the value of b ?

(A) 46
(B) 48
(C) 72
(D) 84
(E) 96

Attachment:

parallelogram.jpg [ 17 KiB | Viewed 511 times ]

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In the figure, ABCD is a parallelogram, what is the value of b ?  [#permalink]

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Updated on: 10 Oct 2018, 00:45
Bunuel wrote:

In the figure, ABCD is a parallelogram, what is the value of b ?

(A) 46
(B) 48
(C) 72
(D) 84
(E) 96

Attachment:
parallelogram.jpg

A =C

B = D.

A = 96

C= 96

A + C= 96*2 = 192.

B + D + 192 = 360

B + B = 168

2B = 168

B = 84.

Originally posted by selim on 10 Oct 2018, 00:41.
Last edited by selim on 10 Oct 2018, 00:45, edited 1 time in total.
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Re: In the figure, ABCD is a parallelogram, what is the value of b ?  [#permalink]

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10 Oct 2018, 00:45
Bunuel wrote:

In the figure, ABCD is a parallelogram, what is the value of b ?

(A) 46
(B) 48
(C) 72
(D) 84
(E) 96

Attachment:
parallelogram.jpg

$$a=48+48=96$$
$$2a=96*2=192$$
as $$2a+2b=360$$
$$2b=360-2a$$
$$2b=360-192$$
$$2b=168$$
$$b=84$$
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Re: In the figure, ABCD is a parallelogram, what is the value of b ?  [#permalink]

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10 Oct 2018, 00:53
Bunuel wrote:

In the figure, ABCD is a parallelogram, what is the value of b ?

(A) 46
(B) 48
(C) 72
(D) 84
(E) 96

Attachment:
parallelogram.jpg

ABCD is parallelogram i.e. Sum of Adjacent two angle = 180º

Angle A = 48+48 = 96

i.e. Angle bº = 180º-96º = 84º

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Re: In the figure, ABCD is a parallelogram, what is the value of b ?  [#permalink]

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13 Oct 2018, 17:31
Bunuel wrote:

In the figure, ABCD is a parallelogram, what is the value of b ?

(A) 46
(B) 48
(C) 72
(D) 84
(E) 96

Attachment:
parallelogram.jpg

We see that angle DAB = 48 + 48 = 96 degrees. Since ABCD is a parallelogram and consecutive angles of a parallelogram are supplementary, angle ABC = 180 - 96 = 84 degrees. So b = 84.

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Re: In the figure, ABCD is a parallelogram, what is the value of b ?   [#permalink] 13 Oct 2018, 17:31
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