The given figure (not drawn to scale) shows two straight lines AB and CD. If equation of the line AB is : y = x + 1 and equation of line CD is : y = $\sqrt{3}$x - 1. Write down the inclination of lines AB and CD; also, find the angle θ between AB and CD.

Given,

Equation of AB :

⇒ y = x + 1

Comparing the above equation with y = mx + c we get,

Slope of AB = 1.

Let θ₁ be the inclination of AB then,

⇒ tan θ₁ = 1

⇒ tan θ₁ = tan 45°

⇒ θ₁ = 45°.

Equation of CD :

⇒ y = $\sqrt{3}$x - 1

Comparing the above equation with y = mx + c we get,

Slope of CD = $\sqrt{3}$.

Let θ₂ be the inclination of AB then,

⇒ tan θ₂ = $\sqrt{3}$

⇒ tan θ₂ = tan 60°

⇒ θ₂ = 60°.

From figure,

∠FGE = 180° - θ₂ = 180° - 60° = 120°.

In △EFG,

∠E + ∠F + ∠G = 180

⇒ θ₁ + θ + 120° = 180°

⇒ 45° + θ + 120° = 180°

⇒ θ + 165° = 180°

⇒ θ = 180° - 165° = 15°.

Hence, inclination of AB is 45°, inclination of CD is 60° and θ = 15°.