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Answer:
Given: and q is a transversal.
Alternative Interior Angle states that a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal are equal.
By alternative interior angle;
Definition of Congruent angles are angles that have the same degree of measurement.
Therefore, [By definition of Congruent] .....[1]
Linear Pair states that a pair of adjacent angles formed when two lines are intersect.
therefore, and
are a linear pair. [by definition of linear pair]
Two angles of linear pairs are always supplementary , which means their measure are add up to 180 degree.
By the definition of supplementary angles, .....[2]
Substitute equation [1] in [2] we get,
By the definition of supplementary angles,
is supplementary to
Hence proved!