In the diagram above, rectangle ABCD is intersected by line WZ at poin

Question

https://gmatclub.com/forum/download/file.php?id=35642 In the diagram above, rectangle ABCD is intersected by line WZ at points X and Y. What is the measure of angle ZYB? (1) Angle CXY + Angle XYB = 270 (2) The measure of angle WXC is equal to the measure of angle AYX. PolygonXYBDC.png

Sammy599 · Answer

Statement 1: this does not provide us with any useful information about angles other than those mentioned. Insufficient.

Statement 2: from this we can draw the conclusion that ang AXY = ang AYX (ang AXY is vertically opposite ang WXC, which in turn is equal to ang AYX as stated). This is insufficient to find the MEASURE of the required angle.

Putting the two together, however, we know that:
ang AXY +ang CXY + ang AYX + ang XYB = 360
Where CXY + XYB = 270
Therefore, AYX + AXY = 90 and consequently AYX is 45.

Finally, ZYB = AYX = 45 ( vertically opposite)
 
The answer should be C.

I would appreciate a kudos if you like my solution!

Leo8 · Answer

FullSizeRender (3).jpg + B

profileusername · Answer

Why can we not apply the exterior angle formula on angle CXY and angle XYB from the information in statement (1) to get the values for angle AXY and angle AYX?

abhimahna · Answer

Hi TheMastermind , Even if you apply the exterior angle formula on statement 1, you will get angle CXY = angle A + angle AYX -- (1) angle XYB = angle A + angle AXY --(2) Adding (1) and (2), I will get, angle CXY + angle XYB = 270 or 2 * angle A + angle AYX + angle AXY = 270 or angle AYX + angle AXY = 270 - 2 (90) or angle AYX + angle AXY = 90. Fine, we already know that the sum of these two angles is 90. So, we didn't find anything special. Now, you cannot say that each of these angles are equal because we don't know whether we have AX = AY. Hence, this method will not yield us what we want. I hope that makes sense.

profileusername · Answer

But the sum of those two angles is equal to 90. Shouldn't that mean that we have an isosceles right angles triangle with sides AX as equal to AY?

abhimahna · Answer

Hi  TheMastermind  ,

No, If the sum of other two angles is 90, that doesn't mean the angles are equal to each other and thus the sides are equal.

What if we have one of the two angles as 30 and the other 60? The sum will still be 90 but the triangle is not an isosceles triangle.

Does that makes sense?

Feel free to ask any doubts, if you have any.

abhimahna · Answer

Hey  spatel2  ,

No, the answer is correct. Please recheck your solution.

bumpbot · Answer

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In the diagram above, rectangle ABCD is intersected by line WZ at poin

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In the diagram above, rectangle ABCD is intersected by line WZ at poin

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