Is triangle XYZ an equilateral triangle?

Question

Is triangle XYZ an equilateral triangle? 
 
(1) Angle X is 60°.
(2) Side XY is equal to side YZ.

Chethan92 · Answer

Statement 1 is insufficient.
No idea about angles X and Y.

From 2: It can be either isoscles or equilateral.

Combining 1&2 is suficient.

C is the answer

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sumit411 · Answer

St1: it can be any triangle as we have restricted only one angle. Other angles can be 60,60 or 40,20

St2: it can be an isosceles triangle or an equilateral triangle.

Combining
Sufficient
C

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EgmatQuantExpert · Answer

Solution

To find:  
 • If triangle XYZ is an equilateral triangle or not

Approach and Working:   
 • In equilateral triangle,
o All sides are equal
o All angles are equal to 60 degrees

Analysing Statement 1  
 • We are given that ∠X = 600
• We do not have information about any other angle
 
Therefore, Statement 1 alone is not sufficient to answer this question

Analysing Statement 2  
 • We are given that XY = YZ
• We do not have any information about the third side, ZX
 
Therefore, Statement 2 alone is not sufficient to find an answer.

Combining Both Statements  
 • Combining both the statements, we get
o XY = YZ, implies ∠Y = ∠Z, and 
o ∠X = 60 degrees, implies ∠Y + ∠Z = 180 – 60 = 120 degrees 
o From the above two equations, we get, ∠Y = ∠Z = 60 degrees 
 
Thus, Statement (1) and (2) TOGETHER are sufficient to answer the question

Hence, the correct answer is option C.

Answer: C

https://e-gmat.com/blogs/wp-content/uploads/2016/12/Geometry-Ability-Quiz-4-e1480581478957.png

CounterSniper · Answer

(1) Angle X is 60°.
no information on sides .
Y+Z =120
insufficient

(2) Side XY is equal to side YZ.
The triangle can be an isosceles or an equilateral triangle
insufficient.

using both the statements.
x=z=60
y=180-120=60
x=y=z=60
sufficient

Is triangle XYZ an equilateral triangle?

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