# HOW TO FIND ANGLE BETWEEN TWO STRAIGHT LINES

How to find angle between two straight lines :

Here we are going to see how to find the angle between two straight lines.

By using the formula given below, we may find the angle between two straight line

θ = tan-1 |(m₁ - m₂)/(1 + m₁ m₂)|

m1 = Slope of 1st line

m2  =  Slope of 2nd line

Note :

If the given two lines are parallel, then angle formed by those lines is 0.

If two lines are perpendicular, the angle between two line is 90.

## How to find angle between two straight lines - Examples

Let us look into some example problems to understand the above concept.

Example 1 :

Find the angle between the straight lines 3x − 2y + 9 = 0 and 2x + y − 9 = 0.

Solution :

3x − 2y + 9 = 0

Slope of 1st line  =  -Coefficient of x/Coefficient of y

=  -3/(-2)  =  3/2

2x + y - 9 = 0

Slope of 2nd line  =  -Coefficient of x/Coefficient of y

=  -2/1  =  -2

By applying the above values in the formula, we get

θ = tan-1 |(3/2) - (-2))/(1 + (3/2) (-2))|

θ = tan-1 |(3/2) + 2))/(1 - 3)|

θ = tan-1 |(3 + 4)/2/(- 2)|

θ = tan-1 |-7/4|

θ = tan-1 (7/4)

Example 2 :

Show that the straight lines 2x + y − 9 = 0 and 2x + y − 10 = 0 are parallel.

Solution :

To show that is the two lines are parallel, let us find ther slopes.

2x + y - 9 = 0

Slope of 1st line  =  -Coe fficient of x/Coefficient of y

=  -1/(-2)  =  1/2  ----(1)

2x + y − 10 = 0

Slope of 2nd line  =  -Coefficient of x/Coefficient of y

=  -1/2  =  -1/2   ------(2)

Since the slopes of given lines are equal, the given lines are parallel.

Hence the angle between the above lines is 0.

Example 3 :

Show that the straight lines 2x + 3y − 9 = 0 and 3x − 2y + 10 = 0 are at right angles.

Solution :

Slope of the straight line 2x + 3y − 9 = 0 is m1 = −2/3

Slope of the straight line 3x – 2y + 10 = 0 is m2 = 3/2

m1 x m2  =  (-2/3) x (3/2)

=  -1

Hence the angle between the above lines is 90 degree.

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