Given, the lines are:

y = x ...........1

y = √3x .......2

From equation 1,

m₁ = 1

and from equation 2,

m₂ = √3

Let θ is the angle between the given lines.

Now tan θ = |m₁ - m₂ |/(1 + m₁ * m₂ )

=> tan θ = |(1 - √3)/(1 + 1 * √3)|

=> tan θ = |(1 - √3)/(1 + √3)|

=> tan θ = |(√3 - 1)/(√3 + 1)|

=> tan θ = |{(√3 - 1)/(√3 + 1)}*{(√3 - 1)/(√3 - 1)}|

=> tan θ = |(√3 - 1)² /(3 - 1)|

=> tan θ = |(3 + 1 - 2√3)/2|

=> tan θ = |(4 - 2√3)/2|

=> tan θ = |2 - √3|

=> tan θ = ±(2 - √3)

=> θ = 15, 165

 So, the angle between the given lines are 15 and 165