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

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