Is the triangle equilateral ?

Question

1. Exterior angle Y is 120

2. Length of the side opposite to vertex Z = Length of the side opposite to vertex X

ShankSouljaBoi · Answer

Sorry for the image guys, I am not good with drawing

Enjoy the question.

Bunuel · Answer

Is it your question or Experts' Global's question? Thank you.

ShankSouljaBoi · Answer

Source is expert's global ( I have appropriately tagged the author in the source category ), but i could not copy the image so i had to make it myself on paint, apparently not very good at drawing . That is the reason i appologized to the community

Bunuel · Answer

Got it. Thank you. The image is pretty good.

Harsh9676 · Answer

IMO C

Statement 1: Did not give any conclusive evidence about the interior angles of X and Z. It just says that the Sum of interior angles of X and Z = 120. X and Z could be anuthing.

St2 : Confirms that length of XY = length of YZ. Therefore the angles opposite to these sides would be equal too.

The triangle could either be an equilateral or an isosceles triangle.

Combined we know that the interior angles of X and Z are equal and X + Z = 120 . Therefore, interior angle of X = 60 , Z = 60 and automatically Y = 60

chetan2u · Answer

Is the triangle equilateral ?

1. Exterior angle Y is 120 
So the interior angle is 180-120=60
It is possible that other two triangles are 60 each and in that case, an equilateral triangle. 
It is also possible other angles are 20 and 100, then NO
Insufficient

2. Length of the side opposite to vertex Z = Length of the side opposite to vertex X
Just tells us that the two angles X and Z are equal. But nothing about Y. 
Insufficient

Combined
Y=60 and X+Z=120
Since X=Z, 2X=120.....X=60
All angles are equal and 60 each, so yes, it is an equilateral triangle.

C

jhavyom · Answer

Is the triangle equilateral ?

1. Exterior angle Y is 120
angle X + angle Z = 120
X and Z may or may not be equal

NOT SUFFICIENT

2. Length of the side opposite to vertex Z = Length of the side opposite to vertex X 
XY = YZ
XZ can take any length

NOT SUFFICIENT

(1) + (2)
XY = YZ, angle X + angle Z = 120 and angle Y = 60
Since, XY = YZ, therefore angle X = angle Z
Now, X+Z = 120 or 2X = 120
X = 60 = Y = Z
So, XYZ is an equilateral triangle

SUFFICIENT

Option C is the answer.

Is the triangle equilateral ?

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