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