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# Which of the following sets of values for w, x, y, and z, respectively

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Math Expert
Joined: 02 Sep 2009
Posts: 50572
Which of the following sets of values for w, x, y, and z, respectively  [#permalink]

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16 Oct 2017, 00:36
00:00

Difficulty:

15% (low)

Question Stats:

89% (00:56) correct 11% (00:30) wrong based on 67 sessions

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Which of the following sets of values for w, x, y, and z, respectively, are possible if ABCD is a parallelogram?

I. 50, 130, 50, 130
II. 60, 110, 70, 120
III. 60, 150, 50, 150

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III

Attachment:

2017-10-16_1235.png [ 5.96 KiB | Viewed 990 times ]

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Re: Which of the following sets of values for w, x, y, and z, respectively  [#permalink]

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16 Oct 2017, 19:19
As the opposite sides(e.g. AD & DC) of a parallelogram are parallel, the angles (e.g. x & y) created by a third side between them will always sum to 180.

Only I satisfies this condition: 50 + 130 = 180.

Ans: A.
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Re: Which of the following sets of values for w, x, y, and z, respectively  [#permalink]

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16 Oct 2017, 21:11
As it is provided in the question, ABCD is a parallelogram, the opposite sides must be equal.
Hence, A is the correct answer.
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Re: Which of the following sets of values for w, x, y, and z, respectively  [#permalink]

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16 Oct 2017, 21:40
parallelogram:
Opposite sides should be equal. So answer must be A

another property: sum of the angles should be 360.
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Re: Which of the following sets of values for w, x, y, and z, respectively  [#permalink]

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17 Oct 2017, 10:54
Bunuel wrote:

Which of the following sets of values for w, x, y, and z, respectively, are possible if ABCD is a parallelogram?

I. 50, 130, 50, 130
II. 60, 110, 70, 120
III. 60, 150, 50, 150

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III

Attachment:
2017-10-16_1235.png

For ABCD to be a parallelogram, not only must the sum of the angle measures be 360 degrees (i.e., w + x + y + z = 360), but also the opposite angles must be equal (i.e., w = y and x = z). Scanning the Roman numerals, we see that II and III do not have equal opposite angles. Thus, we are left with showing whether the numbers in Roman numeral I sum to 360. Since 50 + 130 + 50 + 130 = 360, only Roman numeral I is correct.

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Re: Which of the following sets of values for w, x, y, and z, respectively  [#permalink]

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22 Oct 2017, 14:20

The logic is the four angles must add to 360. In addition, it's a parallelogram. So angle w=y and x=z. Using those two properties, I eliminated II and III.
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Re: Which of the following sets of values for w, x, y, and z, respectively  [#permalink]

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22 Oct 2017, 21:44
Since ABCD is a parallelogram => (x + y + z + w = 360 degrees) and (x= z; y = w)

Only I satisfies both conditions. Hence the answer is A.
Re: Which of the following sets of values for w, x, y, and z, respectively &nbs [#permalink] 22 Oct 2017, 21:44
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