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If quadrilateral WXYZ, above, is a parallelogram, what is the value of

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Bunuel
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If quadrilateral WXYZ, above, is a parallelogram, what is the value of [#permalink] New post   06 Jun 2017, 11:45
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If quadrilateral WXYZ, above, is a parallelogram, what is the value of b?

A. 25
B. 35
C. 45
D. 50
E. 70

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B
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Re: If quadrilateral WXYZ, above, is a parallelogram, what is the value of [#permalink] New post   15 Jun 2017, 16:18
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Bunuel wrote:

If quadrilateral WXYZ, above, is a parallelogram, what is the value of b?

A. 25
B. 35
C. 45
D. 50
E. 70


Referencing the diagram, we see that angle XWZ must be 70 degrees since angle XWZ and the 110-degree angle make up a straight line. We also see that angle XYZ (the 2b-degree angle) must be 70 degrees since opposite angles of a parallelogram are equal in measure. Thus, we have 2b = 70, or b = 35.

Answer: B
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Re: If quadrilateral WXYZ, above, is a parallelogram, what is the value of [#permalink] New post   06 Jun 2017, 12:28
We know that opposite angles in a parallelogram are congruent.
(W=Y and X=Z)

Hence 2b = XWZ = 180 - 110 (Since angles in a straight line add up to a 180)

Since we are asked the value of b,
b = 70/2 = 35(Option B)


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Re: If quadrilateral WXYZ, above, is a parallelogram, what is the value of [#permalink] New post   06 Jun 2017, 12:54
Opposite angles of a ||gm are equal;
Therefore, W=Y

70=2b
=>b=35

Answer => B
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Re: If quadrilateral WXYZ, above, is a parallelogram, what is the value of [#permalink] New post   06 Jun 2017, 14:56
180-110= 70
70 = 2B
b = 35
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Re: If quadrilateral WXYZ, above, is a parallelogram, what is the value of [#permalink] New post   06 Jun 2017, 14:57
180-110= 70
70 = 2B
b = 35
answer B :-D
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Re: If quadrilateral WXYZ, above, is a parallelogram, what is the value of [#permalink] New post   12 Jun 2017, 20:20
\(2B + 110 =180 => 2b=70 => b=\frac{70}{2}=35\)
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Re: If quadrilateral WXYZ, above, is a parallelogram, what is the value of [#permalink] New post   13 Jun 2017, 06:09
2b = 180 -110
=> b =70/2=35
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Re: If quadrilateral WXYZ, above, is a parallelogram, what is the value of [#permalink]
13 Jun 2017, 06:09
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