Parallel lines cut by a transversal problems worksheet

Problem 1 :

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

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.

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 4 :

In the figure given below, let the lines l1 and l2 be parallel and t is transversal. Find the value of 'x'.

1. Answer :

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°

Same side exterior angles are supplementary.

∠1 + ∠8 = 180°

∠2 + ∠7 = 180°

2. Answer :

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°

Substitute ∠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°

3. Answer :

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

4. Answer :

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

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What are the 5 angles formed by parallel lines cut by a transversal?

When any two parallel lines are cut by a transversal, there are various pairs of angles that are formed. These angles are corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles.

What 3 things happen when parallel lines are cut by a transversal?

If two parallel lines are cut by a transversal, then, Alternate Interior Angles are congruent. If two parallel lines are cut by a transversal, then, Alternate Exterior Angles are congruent. If two parallel lines are cut by a transversal, then corresponding angles are congruent.