Solution:

Given line equations, y = x + 1 and y = √3x – 1

On comparing with y = mx + c,

The slope of the line: y = x + 1 is 1 as m = 1

So, tan θ = 1 ⇒ θ = 45^o

And,

The slope of the line: y = √3x – 1 is √3 as m = √3

So, tan θ = √3 ⇒ θ = 60^o

Now, in triangle formed by the given two lines and x-axis

Ext. angle = Sum of interior opposite angle

60^o = θ + 45^o

θ = 60^o – 45^o

Thus, θ = 15^o