# Parallel and Transversal Lines

Here we discuss how the angles formed between parallel and transversal lines.

When the transversal intersects two parallel lines:

• Pairs of corresponding angles are equal.

• Pairs of alternate angles are equal

• Interior angles on the same side of transversal are supplementary.

Worked-out problems for solving parallel and transversal lines:

1. In adjoining figure l ∥ m is cut by the transversal t. If ∠1 = 70, find the measure of ∠3, ∠5, ∠6.

Solution:

We have ∠1 = 70°

∠1 = ∠3 (Vertically opposite angles)

Therefore, ∠3 = 70°

Now, ∠1 = ∠5 (Corresponding angles)

Therefore, ∠5 = 70°

Also, ∠3 + ∠6 = 180° (Co-interior angles)

70° + ∠6 = 180°

Therefore, ∠6 = 180° - 70° = 110°

2. In the given figure AB ∥ CD, ∠BEO = 125°, ∠CFO = 40°. Find the measure of ∠EOF.

Solution:

Draw a line XY parallel to AB and CD passing through O such that AB ∥ XY and CD ∥ XY

∠BEO + ∠YOE = 180° (Co-interior angles)

Therefore, 125° + ∠YOE = 180°

Therefore, ∠YOE = 180° - 125° = 55°

Also, ∠CFO = ∠YOF (Alternate angles)

Given ∠CFO = 40°

Therefore, ∠YOF = 40°

Then ∠EOF = ∠EOY + ∠FOY

= 55° + 40° = 95°

3. In the given figure AB ∥ CD ∥ EF and AE ⊥ AB.

Also, ∠BAE = 90°. Find the values of ∠x, ∠y and ∠z.

Solution:

y + 45° = 1800

Therefore, ∠y = 180° - 45° (Co-interior angles)

= 135°

∠y =∠x (Corresponding angles)

Therefore, ∠x = 135°

Also, 90° + ∠z + 45° = 180°

Therefore, 135° + ∠z = 180°

Therefore, ∠z = 180° - 135° = 45°

4. In the given figure, AB ∥ ED, ED ∥ FG, EF ∥ CD
Also, ∠1 = 60°, ∠3 = 55°, then find ∠2, ∠4, ∠5.

Solution:

Since, EF ∥ CD cut by transversal ED

Therefore, ∠3 = ∠5 we know, ∠3 = 55°

Therefore, ∠5 = 55°

Also, ED ∥ XY cut by transversal CD

Therefore, ∠5 = ∠x we know ∠5 = 55°

Therefore,∠x = 55°

Also, ∠x + ∠1 + ∠y = 180°

55° + 60° + ∠y = 180°

115° + ∠y = 180°

∠y = 180° - 115°

Therefore, ∠y = 65°

Now, ∠y + ∠2 = 1800 (Co-interior angles)

65° + ∠2 = 180°

∠2 = 180° - 65°

∠2 = 115°

Since, ED ∥ FG cut by transversal EF

Therefore, ∠3 + ∠4 = 180°

55° + ∠4 = 180°

Therefore, ∠4 = 180° - 55° = 125°

5. In the given figure PQ ∥ XY. Also, y : z = 4 : 5 find.

Solution:

Let the common ratio be a

Then y = 4a and z = 5a

Also, ∠z = ∠m (Alternate interior angles)

Since, z = 5a

Therefore, ∠m = 5a [RS ∥ XY cut by transversal t]

Now, ∠m = ∠x (Corresponding angles)

Since, ∠m = 5a

Therefore, ∠x = 5a [PQ ∥ RS cut by transversal t]

∠x + ∠y = 180° (Co-interior angles)

5a + 4a = 1800

9a = 180°

a = 180/9

a = 20

Since, y = 4a

Therefore, y = 4 × 20

y = 80°

z = 5a

Therefore, z = 5 × 20

z = 100°

x = 5a

Therefore, x = 5 × 20

x = 100°

Therefore, ∠x = 100°, ∠y = 80°, ∠z = 100°

Lines and Angles

Fundamental Geometrical Concepts

Angles

Classification of Angles

Related Angles

Some Geometric Terms and Results

Complementary Angles

Supplementary Angles

Complementary and Supplementary Angles

Linear Pair of Angles

Vertically Opposite Angles

Parallel Lines

Transversal Line

Parallel and Transversal Lines

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Comparison of Three-digit Numbers | Arrange 3-digit Numbers |Questions

Sep 13, 24 02:48 AM

What are the rules for the comparison of three-digit numbers? (i) The numbers having less than three digits are always smaller than the numbers having three digits as:

2. ### Worksheet on Three-digit Numbers | Write the Missing Numbers | Pattern

Sep 13, 24 02:23 AM

Practice the questions given in worksheet on three-digit numbers. The questions are based on writing the missing number in the correct order, patterns, 3-digit number in words, number names in figures…

3. ### 2nd Grade Place Value | Definition | Explanation | Examples |Worksheet

Sep 13, 24 01:20 AM

The value of a digit in a given number depends on its place or position in the number. This value is called its place value.

4. ### Comparison of Two-digit Numbers | Arrange 2-digit Numbers | Examples

Sep 12, 24 03:07 PM

What are the rules for the comparison of two-digit numbers? We know that a two-digit number is always greater than a single digit number. But, when both the numbers are two-digit numbers