In the triangle above, what is the measure of Angle YZX?

Question

https://gmatclub.com/forum/download/file.php?id=54523 In the triangle above, what is the measure of Angle YZX? (1) Angle YWX = angle WYX = 30° (2) Triangles WXY and XYZ are isosceles triangles Are You Up For the Challenge: 700 Level Questions 476627_edd67534-de02-4e99-beb2-025a85e2aa37_lg.png

chetan2u · Answer

(1) Angle YWX = angle WYX = 30°
So the third angle WXY=180-30-30=120, and the complementary \ angle YXZ=180-120=60 .
Now  \angle{XYZ}=90-30=60 .
Therefore,  \angle YZX=180-60-60=60 .
Suff

(2) Triangles WXY and XYZ are isosceles triangles
The  \angle YZX  will depend on the  \angle XYZ , which cannot be found.
Insuff

A

uchihaitachi · Answer

Statement 1  
We know the values of  \angle YWX  and  \angle WYX . From this, we can find the value of  \angle YZX  and we will get a unique value. 
 Sufficient

Statement 2 
We don't know which two sides out of the three of each of the triangles WXY and XYZ are equal. 
Therefore, we can get multiple values of the  \angle YZX . 
 Insufficient

IMO, A

CrackverbalGMAT · Answer

The bigger triangle WYZ is a right-angled triangle, right angled at Y. Therefore, angle W + angle Z = 90 degrees.

From statement I alone, angle YWX = angle WYX = 30 degree. 
This means, angle W = 30 degrees. Therefore, angle Z = 60 degrees. 
Statement I alone is sufficient to find the measure of angle YZX. Answer options B, C and E can be eliminated. Possible answer options are A or D.

From statement II alone, triangles WXY and XYZ are isosceles triangles. 
Since we do not know the equal sides of the isosceles triangles, we cannot determine the angles and hence, cannot determine the measure of angle Z.
Statement II alone is insufficient. Answer option D can be eliminated.

The correct answer option is A .

Hope that helps!

PriyaLon · Answer

Whilst I agree that Statement 1 is sufficient in itself, I am confused about Statement 2 as it contradicts Statement 1.

I understood that 1) and 2) are "Truths" whether or not they give you sufficient data. Since Statement 2 states that the triangles are isosceles, and isosceles triangles have two equal base angles and one different vertex angle, all three angles cannot be the same (i.e. 60 degrees) as per Statement 1.

Am I getting something very wrong here? Sorry for the confusion if so.

SiddharthR · Answer

Hello Priya,

When they say WXY & XYZ are isosceles, you cannot assume two sides are equal to each other. For example, triangle WXY can have the following 2 sides equal --> WX, XY; WY, XY; WX, WY. The same goes for the other triangle XYZ.

Since you do not know what sides are equal, you cannot calculate the final angle.

In the triangle above, what is the measure of Angle YZX?

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