# Angles in Parallel Lines

See how to find the angles formed by parallel lines and a transversal.

6 examples and their solutions.

## Angles in Parallel Lines

### Property

m∠1 = m∠1' = m∠3 = m∠3'

m∠2 = m∠2' = m∠4 = m∠4'

## Corresponding Angles

### Definition

m∠1 = m∠1'

m∠2 = m∠2'

m∠3 = m∠3'

m∠4 = m∠4'

m∠1 and m∠1'

m∠2 and m∠2'

m∠3 and m∠3'

m∠4 and m∠4'

### Example

7x + 1 = 64

7x = 63

x = 9

Close

### Example

14x - 3 = 8x + 45 - [1]

6x = 48

x = 8

[1]

(14x - 3) = θ

(8x + 45) = θ

(8x + 45) = θ

Close

## Alternate Interior Angles

### Definition

m∠1 = m∠1'

m∠2 = m∠2'

m∠1 and m∠1'

m∠2 and m∠2'

### Example

6x - 7 = 59

6x = 66

x = 11

Close

### Example

x = 53 + 34

= 87

[1]

Draw an auxiliary line (dashed line)

that is parallel to the horizontal lines

and that passes through the middle angle.

The blue angles are congruent.

So the bottom blue angle is 53°.

And the green angles are congruent.

So the top green angle is 34°.

that is parallel to the horizontal lines

and that passes through the middle angle.

The blue angles are congruent.

So the bottom blue angle is 53°.

And the green angles are congruent.

So the top green angle is 34°.

Close

## Alternate Exterior Angles

### Definition

m∠1 = m∠1'

m∠2 = m∠2'

m∠1 and m∠1'

m∠2 and m∠2'

### Example

8x + 10 = 74

8x = 64

x = 8

Close

## Consecutive Interior Angles

### Definition

m∠1 + m∠2 = 180

m∠1' + m∠2' = 180

m∠1 and m∠2

m∠1' and m∠2'

### Example

5x + 60 + 70 = 180

5x + 130 = 180

5x = 50

x = 10

Close