**Parallel lines and transversals**

A transversal is a line that intersects two lines in the same plane at two different points. Transversal and lines l₁ and l₂ form eight angles.

More clearly,

Here, l₁ and l₂ are parallel lines.

From the above figure, we have the following important points.

Vertically opposite angles are equal. |
< 1 = < 3 < 2 = < 4 < 5 = < 7 < 6 = < 8 |

Corresponding angles are equal. |
< 1 = < 5 < 2 = < 6 < 3 = < 7 < 4 = < 8 |

Alternate interior angles are equal. |
< 3 = < 5 < 4 = < 6 |

Alternate exterior angles are equal. |
< 1 = < 7 < 2 = < 8 |

Consecutive interior angles are supplementary. |
< 3 + < 6 = 180° < 4 + < 5 = 180° |

**Example 1 :**

In the figure given below, let the lines l₁ and l₂ be parallel and m is transversal. If ∠F = 65°, find the measure of each of the remaining angles.

**Solution : **

From the given figure,

∠F and ∠H are vertically opposite angles and they are equal.

Then, ∠H = ∠F -------> ∠H = 65°

∠H and ∠D are corresponding angles and they are equal.

Then, ∠D = ∠H -------> ∠D = 65°

∠D and ∠B are vertically opposite angles and they are equal.

Then, ∠B = ∠D -------> ∠B = 65°

∠F and ∠E are together form a straight angle.

Then, we have

∠F + ∠E = 180°

Plug ∠F = 65°

∠F + ∠E = 180°

65° + ∠E = 180°

∠E = 115°

∠E and ∠G are vertically opposite angles and they are equal.

Then, ∠G = ∠E -------> ∠G = 115°

∠G and ∠C are corresponding angles and they are equal.

Then, ∠C = ∠G -------> ∠C = 115°

∠C and ∠A are vertically opposite angles and they are equal.

Then, ∠A = ∠C -------> ∠A = 115°

Therefore,

∠A = ∠C = ∠E = ∠G = 115°

∠B = ∠D = ∠F = ∠H = 65°

**Example 2 :**

In the figure given below, let the lines l₁ and l₂ be parallel and t is transversal. Find the value of "x"

**Solution : **

From the given figure,

∠(2x + 20)° and ∠(3x - 10)° are corresponding angles.

So, they are equal.

Then, we have

2x + 20 = 3x - 10

30 = x

Hence, x = 30°

**Example 3 :**

In the figure given below, let the lines l₁ and l₂ be parallel and t is transversal. Find the value of "x".

**Solution : **

From the given figure,

∠(3x + 20)° and ∠2x° are consecutive interior angles.

So, they are supplementary.

Then, we have

3x + 20 + 2x = 180°

5x + 20 = 180°

5x = 160°

x = 32°

Hence, x = 32°

After having gone through the stuff given above, we hope that the students would have understood "Parallel lines and transversals".

Apart from the stuff given above, if you want to know more about "Parallel lines and transversals", please click here

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

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**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**

**Time and work 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**