Find the acute angle between the lines 2x – y + 3 = 0 and x + y + 2 = 0.

Given:

The equations of the lines are

2x − y + 3 = 0 … (1)

x + y + 2 = 0 … (2)

To find:

Angles between two lines.

Explanation:

Let m₁ and m₂ be the slopes of these lines.

m₁ = 2, m₂ = -1

Let θ be the angle between the lines.
Then,

⇒

Hence, the acute angle between the lines is