A 2 min read

Solution

Steps 1 & 2: Understand Question and Draw Inferences

We are given:

• Three intersecting lines, as shown in the diagram.
• And, the angles between these 3 lines.

We need to find:

• The value of x.

Let us name all the three lines as L₁, L₂, and L₃ as shown:

• One angle between line L₁ and L₂ is x⁰.
• Similarly, one angle between line L₂ and L₃ is z⁰.
• And, one angle between line L₁ and L₃ is y⁰.
  • Hence, their vertically opposite angles will also be equal as shown in diagram below.

• Therefore, by applying the property that sum of all the angles around a point is 360⁰, we can say that:
  • 2x + 2y + 2z = 360⁰
  • Or, x + y + z = 180⁰

To find value of x, we need the value of y and z.

With this understanding, let us now analyse the individual statements.

 

Step 3: Analyse Statement 1

“x = y = z”

• x + x + x = 180⁰
  • 3x = 180⁰
  • From this equation, we can find the value of x.

Thus, statement 1 is sufficient to answer the question.

 

Step 4: Analyse Statement 2

“z = 60”

Since we do not know the value of y, we cannot find the value of x.

Thus, statement 2 is not sufficient to answer the question.

 

Step 5: Combine Both Statements Together (If Needed)

As we could determine the answer from statement 1 individually, this step is not required.

Hence, the correct answer is option A.

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