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## Parallel lines

Below is a typical diagram with parallel lines.

The parallel lines are marked with arrows and the line that crosses them is called the transversal.

Also notice that the angles are either obtuse or acute.  All the acute angles are equal and all the obtuse angles are equal.  Also any acute plus any obtuse angle equals $180^o$.

## Pairs of angles

### Corresponding Angles

Are in the same position on each parallel line

### Alternate Angles

Are on oppisite sides of the transversal touching each parallel line

### Co-interior Angles

On the same side of the transversal between the parallel lines

### Examples

Find the values of the unknowns

$x=79^o \because \mbox{ Alternate angles are equal.}$

$x=37^o \because \mbox{ Corresponding angles are equal.}$

$x = 180^o-51^o-62^o=67^o \hspace{36 pt}\because 180^o\hspace{5 pt}\mbox{in a } \triangle$

$y=67^o \hspace{136 pt}\because \mbox{Corresponding angles are equal.}$

$z=180^o-67^o=113^o \hspace{62 pt}\because 180^o\hspace{5 pt}\mbox{on a line}$