## Angle Between TwoStraight Lines

In this page angle between twostraight lines we are going to see how to find the angle formed  two straight lines.First let us see the formula.

θ = tan-¹ |(m₁ - m₂)/(1 + m₁ m₂)|

Here m₁ is slope of the first line and m₂ is the slope of the second line.To find angle between two lines first we need to find slope of both lines separately and then we have to apply their values in the above formula. Here you can find two example problems to understand this topic clearly.

### Angle between two straight lines:                   Examples

Example 1:

Find the angle between twostraight lines  x + 2y -1=0 and 3x - 2y +5=0

Solution:

To find the angle between two lines we have to find the slopes of the two lines.

Slope of a line = - coefficient of x/coefficient of y

Slope of the fist line  x + 2y -1 = 0

m₁ = -1/2

Slope of the second line 3x - 2y +5=0

m₂ = -3/(-2)

m₂ = 3/2

Angle between the lines

θ = tan-¹ |(m₁ - m₂)/(1 + m₁ m₂)|

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

θ = tan-¹ |[(-1 - 3)/2] /[1 + (-3/4)]|

θ = tan-¹ |[(-4)/2] /[4 + (-3)/4)]|

θ = tan-¹ |[(-2) /[1/4)]|

θ = tan-¹ |[(-2) x[4/1]|

θ = tan-¹ |-8|

θ = tan-¹ (-8)

Example 2:

Find the angle between the lines 2x + y = 4 and x + 3y = 5

Solution:

To find the angle between two lines we have to find the slopes of the two lines.

Slope of a line = - coefficient of x/coefficient of y

Slope of the fist line  2x + y = 4 = 0

m₁ = -2/1

m₁ = -2

Slope of the second line x + 3y = 5

m₂ = -1/3

Angle between the lines

θ = tan-¹ |(m₁ - m₂)/(1 + m₁ m₂)|

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

θ = tan-¹ |[(-2 + 1/3)] /[1 + (2/3)]|

θ = tan-¹ |[(-6+1)/3] /[(3 + 2)/3)]|

θ = tan-¹ |[(-5/3) /[5/3)]|

θ = tan-¹ |[(-5/3) x[3/5]|

θ = tan-¹ |-1|

θ = tan-¹ (1)

θ = 45°          angle between twostraight lines

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