**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 1 ^{st} line**

**m2 = Slope of 2 ^{nd} 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.

**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 1^{st} line = -Coefficient of x/Coefficient of y

= -3/(-2) = 3/2

2x + y - 9 = 0

Slope of 2^{nd} 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 1^{st} line = -Coe fficient of x/Coefficient of y

= -1/(-2) = 1/2 ----(1)

2x + y − 10 = 0

Slope of 2^{nd} 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 m_{1} = −2/3

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

m_{1} x m_{2} = (-2/3) x (3/2)

= -1

Hence the angle between the above lines is 90 degree.

After having gone through the stuff given above, we hope that the students would have understood "How to find angle between two straight lines".

Apart from the stuff given above, if you want to know more about "How to find angle between two straight lines" Please click here.

If you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**