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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.

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, 14:20

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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I'd love to hear any feedback or ways to improve my problem solving. I make a lot of silly mistakes. If you've had luck improving on stupid mistakes, I'd love to hear how you did it.