This question is Based on Equation of a Straight Line Chapter of M.L Aggarwal book for ICSE BOARD for class 10.
In this question a figure is given which represents the line for which equation is given in the question.
So you have to find the angles which the lines make with the positive direction of the x-axis and also determine theta.
This is the Question Number 09 Exercise 12.1 of M.L Aggarwal.
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 = 45o
And,
The slope of the line: y = √3x – 1 is √3 as m = √3
So, tan θ = √3 ⇒ θ = 60o
Now, in triangle formed by the given two lines and x-axis
Ext. angle = Sum of interior opposite angle
60o = θ + 45o
θ = 60o – 45o
Thus, θ = 15o