When two lines are parallel the angles made by a third line crossing them have certain properties.
Corresponding angles
Corresponding angles on parallel lines are equal.
The following diagram shows the four possible pairs of corresponding angles.
Alternate angles
Alternate angles on parallel lines are equal.
The following diagram shows the two possible pairs of alternate angles.
Cointerior angles
Cointerior angles on parallel lines are add up to 180^{o} (supplementary angles).
The following diagram shows the two possible pairs of cointerior angles.
Using these angle properties, the size of angles on parallel lines can be found.
Examples
Example One

Example Two

Example Three




x = 105^{o}
Reason: Corresponding angles on parallel lines are equal.

y = 65^{o}
Reason: Alternate angles on parallel lines are equal.
z + y = 180 z + 65 = 180 z = 115^{o}
Reason: Angles on a staraight line add up to 180 degrees.

w + 75 = 180 w = 105^{o}
Reason: Cointerior angles on parallel lines add up to 180^{o}
t = 105^{o}
Reason: Vertically opposite angles are equal.
