**Parallel lines and transversal worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on parallel lines and transversals.

1. Identify the pairs of angles in the diagram. Then make a conjecture about their angle measures.

2. 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.

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

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

**Problem 1 : **

Identify the pairs of angles in the diagram. Then make a conjecture about their angle measures.

**Solution :**

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 2 :**

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 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,

∠(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 4 :**

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°

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