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.

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

Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life. They are:

It subtracts sadness and adds happiness in our life.

It divides sorrow and multiplies forgiveness and love.

Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”

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