The Angles between two lines is defined as shown below: |

⇒ tan∅ = tan (a

_{2}– a

_{1}),

= (tan a

_{2}- tan a

_{1})/ (1 + tan a

_{1}tan a

_{2 })

To find the angle between two lines we have to follow the steps explained below:

**Step1:**To find the angle first of all we have to assume the angle between two lines.

**Step2:**Then find the value of slopes of the given lines. Let the line be ‘A

_{1}’ and ‘A

_{2}’.

**Step3:**Now determine the Tangent difference between two angles using trigonometric Functions.

**Step4:**Using these steps we can easily get the angle between two lines.

We know that,

a

_{2}= a

_{1}+ ∅,

∅ = a

_{2}– a

_{1},

Now, calculate the value of slopes of line ‘A

_{1}’ and ‘A

_{2}’.

Using trigonometric Functions:

tan∅ = tan (a

_{2}– a

_{1}),

=(tan a

_{2}- tan a

_{1})/ (1 + tan a

_{1}tan a

_{2 })

If tan a

_{1}= m

_{1}(m

_{1}is the Slope of the line A

_{1})

⇒ tan a

_{2}= m

_{2}(m

_{2}is the Slope of the line A

_{2})

So, value of ‘m

_{2}’ is greater than ‘m

_{1}’, (m

_{2}> m

_{1}).

Substitute these values in the given equation and we get:

Tan ∅ = (m

_{2}-m

_{1})/ ( 1 + m

_{1}m

_{2})

Using this formula we find angles between two lines.

Suppose the value of m

_{1}= ½ and m

_{2}= 4 t and we have to find the angle between two lines m

_{1}and m

_{2}?

We know that the value of m

_{2}is always equal to the value of m

_{1.}

Given, m

_{1}= ½ and m

_{2}= 4, the formula to find the angle between two lines is given as:

tan∅ = (m

_{2}-m

_{1})/ ( 1 + m

_{1}m

_{2})

Plug in value of m

_{1}and m

_{2}in the given formula:

Tan ∅ = {4-(1/2)}/(1 + ½ * 4),

={(8-1)/2}/(1 + 2),

tan∅ = 7/6.

This is all about the angle between two line formula and how to use it while solving problems related to it.