Find the angle between the lines and .

Given equations are:-

y = (2 - √3)(x + 5)

⇒ y = (2 - √3)x + (2 - √3)5 …(i)

and y = (2 + √3)(x – 7)

⇒ y = (2 + √3)x – 7(2 + √3) …(ii)

Now, we have to find the slope of eq. (i)

Since, the eq. (i) is in y = mx + b form, we can easily see that the slope (m₁) is (2 - √3)

Now, the slope (m₂) of eq. (ii) is (2 + √3)

Let θ be the angle between the given two lines.

Putting the values of m₁ and m₂ in above eq., we get

[∵(a – b)(a + b) = (a² – b²)]

⇒ tan θ = √3

⇒ θ = tan^-1(√3)

⇒ θ = 60°

Hence, the required angle is 60°