**Parallel lines cut by a 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 : **

**Corresponding Angles : **

∠CGE and ∠AHG, ∠DGE and ∠BHG, ∠CGH and ∠AHF, ∠DGH and ∠BHF ; congruent.

**Alternate interior angles :**

∠CGH and ∠BHG, ∠DGH and ∠AHG ; congruent.

**Alternate exterior angles :**

∠CGE and ∠BHF, ∠DGE and ∠AHF ; congruent.

**Same-side interior angles :**

∠CGH and ∠AHG, ∠DGH and ∠BHG ; supplementary.

**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°

After having gone through the stuff given above, we hope that the students would have understood "Parallel lines cut by a transversal worksheet".

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