A. and
are congruent because they are opposite to one another across the intersection of lines C and D. (We call
and
a "vertical angle pair".)
B. For the same reason and
are congruent, we know that the angles with measures
and
are also congruent. This means
, which we can solve for
.
C.
While vertical angle pairs are congruent, adjacent angle pairs are supplementary. This means that and the measure of
(or
) add to 180 degrees. Similarly,
and the measure of
(or
) also add to 180 degrees.
With , we find