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Is the triangle equilateral ?

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ShankSouljaBoi
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Is the triangle equilateral ? [#permalink] New post   31 Oct 2020, 09:30
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84% (00:56) correct 16% (01:06) wrong based on 58 sessions
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Is the triangle equilateral ?

1. Exterior angle Y is 120

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

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Re: Is the triangle equilateral ? [#permalink] New post   31 Oct 2020, 09:31
Sorry for the image guys, I am not good with drawing :P

Enjoy the question.
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Re: Is the triangle equilateral ? [#permalink] New post   31 Oct 2020, 09:33
Expert Reply
ShankSouljaBoi wrote:
Sorry for the image guys, I am not good with drawing :P

Enjoy the question.


Is it your question or Experts' Global's question? Thank you.
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Is the triangle equilateral ? [#permalink] New post   Updated on: 31 Oct 2020, 09:37
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Bunuel wrote:
ShankSouljaBoi wrote:
Sorry for the image guys, I am not good with drawing :P

Enjoy the question.


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

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 :)

Originally posted by ShankSouljaBoi on 31 Oct 2020, 09:34.
Last edited by ShankSouljaBoi on 31 Oct 2020, 09:37, edited 1 time in total.
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Re: Is the triangle equilateral ? [#permalink] New post   31 Oct 2020, 09:37
Expert Reply
ShankSouljaBoi wrote:
Bunuel wrote:
ShankSouljaBoi wrote:
Sorry for the image guys, I am not good with drawing :P

Enjoy the question.


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

Source is expert's global but i could not copy the image so i had to make it myself on paint, but i am not very good at it . That is the reason i appologized to the community :)


Got it. Thank you. The image is pretty good. :)
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Re: Is the triangle equilateral ? [#permalink] New post   31 Oct 2020, 09:47
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
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Re: Is the triangle equilateral ? [#permalink] New post   31 Oct 2020, 09:48
Expert Reply
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
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Re: Is the triangle equilateral ? [#permalink] New post   31 Oct 2020, 23:17
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.
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Re: Is the triangle equilateral ? [#permalink]
31 Oct 2020, 23:17
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Bunuel
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