# How to Solve Parallel Lines and Transversals Problems? (+FREE Worksheet!)

When a line (transversal) intersects two parallel lines in the same plane, eight angles are formed. In this article, we will teach you how to find the missing angles in this case by using the Parallel Lines and Transversals rules.

## Related Topics

- Special Right Triangles
- How to Solve Triangles Problems
- How to Find Volume and Surface Area of Cubes
- How to Calculate Cylinder Volume and Surface Area
- How to Find Complementary and Supplementary Angles

## A step-by-step guide to solving Parallel Lines and Transversals Problem

- When a line (transversal) intersects two parallel lines in the same plane, eight angles are formed. In the following diagram, a transversal intersects two parallel lines. Angles 1, 3, 5, and 7 are congruent. Angles 2, 4, 6, and 8 are also congruent.
- In the following diagram, the following angles are supplementary angles (their sum is 180):

• Angles 1 and 8

• Angles 2 and 7

• Angles 3 and 6

• Angles 4 and 5

## Examples

### Parallel Lines and Transversals – Example 1:

In the following diagram, two parallel lines are cut by a transversal. What is the value of \(x\)?

**Solution**:

The two angles \(3x-15\) and \(2x+7\) are equivalent.

That is: \(3x-15=2x+7\)

Now, solve for \(x: 3x-15+15=2x+7+15 →\)

\(3x=2x+22→3x-2x=2x+22-2x→x=22\)

### Parallel Lines and Transversals – Example 2:

In the following diagram, two parallel lines are cut by a transversal. What is the value of \(x\)?

**Solution**:

The two angles \(75^\circ\) and \(11x-2\) are equal. \(11x-2=75\)

Now, solve for \(x: 11x-2+2=75+2→ 11x=77→x=\frac{77}{11}→x=7\)

### Parallel Lines and Transversals – Example 3:

In the following diagram, two parallel lines are cut by a transversal. What is the value of \(x\)?

**Solution**:

The two angles \(7x-35\) and \(3x+45\) are equivalents.

That is: \(7x-35=3x+45\)

Now, solve for \(x: 7x-35+35=3x+45+35 →\)

\(7x=3x+80→7x-3x=3x+80-3x→4x=80→x=\frac{80}{4}→x=20\)

### Parallel Lines and Transversals – Example 4:

In the following diagram, two parallel lines are cut by a transversal. What is the value of \(x\)?

**Solution**:

The two angles \(3x-27\) and \(-x+33\) are equivalents.

That is: \(3x-27=-x+33\)

Now, solve for \(x: 3x-27+27=-x+33+27 →\)

\(3x=-x+60→3x+x=-x+60+x→4x=60→x=\frac{60}{4}→x=15\)

## Exercises for Parallel Lines and Transversals

### Find missing angles with Parallel Lines and Transversals.

1.Find the measure of the angle indicated.

2. Solve for \(x\).

3. Find the measure of the angle indicated.

4. Solve for \(x\).

1.\(\color{blue}{110^\circ}\)

2.\(\color{blue}{x=8}\)

3. \(\color{blue}{84^\circ}\)

4.\(\color{blue}{x=5}\)

## Related to This Article

### More math articles

- 10 Most Common 3rd Grade IAR Math Questions
- How to Manage Your Time Effectively on the GED Math Test?
- AFOQT Math FREE Sample Practice Questions
- Top 10 SHSAT Math Practice Questions
- 8th Grade PACE Math Worksheets: FREE & Printable
- How to Draw Geometric Shapes with given condition?
- How tо Buу thе Right Lарtор: A Stер-bу-Stер Guide
- The Ultimate ATI TEAS 7 Math Formula Cheat Sheet
- Adding 2-Digit Numbers
- Algebra Puzzle – Challenge 43

## What people say about "How to Solve Parallel Lines and Transversals Problems? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.