Transversal lines worksheet is much useful to the kids who would like to practice problems on parallel lines.

Before, we look at the worksheet, first let us come to know, what is transversal.

A straight line that intersects two or more straight lines at distinct points is called as transversal.

More clearly,

A straight line intersecting two 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° |

**Problem 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.

**Problem 2 :**

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

**Problem 3 :**

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

**Problem 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°**

**Problem 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°**

**Problem 3 :**

**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 "Transversal lines worksheet".

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