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[b]Q. (Geometry)[/b] w, x, y, and z are depicted as shown in the above figure..

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by Max@Math Revolution » Wed Sep 02, 2020 5:35 am

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Q. (Geometry)

PS- Angles.jpg
w, x, y, and z are depicted as shown in the above figure. Which one of the following is always true?

A. x + y = \(180^o\)
B. w + z = \(180^o\)
C. x + y < z + w
D. x + y = z + w
E. x + y > z + w
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Source: — Data Sufficiency |
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Re: [b]Q. (Geometry)[/b] w, x, y, and z are depicted as shown in the above figure..

by Max@Math Revolution » Mon Sep 14, 2020 5:22 am
Solution:

\(\angle ADC\) + w = \(180^o\) (Measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.)

So, we get \(\angle ADC\) = \(180^o\) - w and similarly, \(\angle BCD\) = \(180^o\) - z.

ABCD is a quadrilateral, and the sum of all the angles of a quadrilateral is equal to \(360^o\). Therefore, we get

y + x + \(180^o\) - w + [m] \(180^o\) - z = \(360^o\)

=> y + x – (w + z) = \(360^o\) – \(360^o\)

=> y + x – (w + z) = 0

=> y + x = w + z

Therefore, D is the correct answer.

Answer: D
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