#
If two parallel lines are cut by a transversal, then each pair of alternate interior angles are

a. congruent

b. supplementary

In the figure above, Line l and m are parallel to each other and is cut by traversal n.

angle 1 and angle 4 are pair of alternate interior angle

$\angle 1+\angle 2=180\xb0..............eq1(Linearpairofangle)\phantom{\rule{0ex}{0ex}}\angle 4+\angle 2=180\xb0.............eq2(sumofinterioranglesonthesamesideoftraversalis180\xb0)\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}fromeq1andeq2,weget,\phantom{\rule{0ex}{0ex}}\angle 1=\angle 4\phantom{\rule{0ex}{0ex}}$

Here we can see that alternate interior angles are equal or congruent.

Regards,

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