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 Tansversal of parallel lines If two lines are cut by a transversal, the corresponding angles are congruent. Note that single or double arrowheads on the lines identify them as being parallel. That means that in the preceding figure, $\angle\;1$ is congruent to $\angle\;5$, $\angle\;2$ is congruent to $\angle\;6$, $\angle\;3$ is congruent to $\angle\;7$, and $\angle\;4$ is congruent to $\angle\;8$. It will be useful to know: If parallel lines are cut by a transversal, their alternate interior angles are congruent. If parallel lines are cut by a transversal, their alternate exterior angles are congruent. If parallel lines are cut by a transversal, their consecutive interior angles are supplementary. If parallel lines are cut by a transversal, their consecutive exterior angles are supplementary. Suppose $m\angle\;2=60^o$. Find $m\angle\;6$. $\angle\;6$ is a corresponding angle to $\angle\;2$ so they are congruent. Therefore $m\angle\;6=60^o$ Suppose $m\angle\;6=50^o$. Find $m\angle\;3$. Angles 3 and 6 are alternate interior angles, so they are congruent. Therefore $m\angle\;3=50^o$ Suppose $m\angle\;7=70^o$. Find $m\angle\;1$. Angles 7 and 1 are consecutive exterior angles, and therefore, they are supplementary. Therefore $m\angle\;1=180^o-70^o=110^o$