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Which of the following sets of values for w, x, y, and z, respectively [#permalink]
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16 Oct 2017, 01:36
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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:
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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, 20:19
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, 22:11
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, 22:40
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, 11:54
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: 20171016_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. Answer: 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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22 Oct 2017, 15:20
A is my answer. 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, 22:44
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
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22 Oct 2017, 22:44






