In the figure above and
are parallel. What is
in terms of
and
?
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The correct answer is A.
Let be the point of intersection of lines
and
.
One way to determine in terms of
and
is to find the measure of each of the angles of
in terms of
,
and
and then apply the triangle sum theorem. Since
is supplementary to
and the measure of
is given to be
, the measure of
is
. Since line
is a transversal to the parallel lines
and
, the alternate interior angles
and
are of equal measure. Thus the measure of
is
, which is also the measure of
. The measure of
is given to be
. Therefore, the sum of the angle measures of
, in degrees, is
. The triangle sum theorem applied to
gives the equation
, which can be solved for
to arrive at
.
Alternatively, one can apply the interior angle sum theorem to pentagon . Since line
is a transversal to the parallel lines
and
, it follows that
and
are supplementary; that is, the sum of the measures of these two angles is
The measure of
, interior to polygon
, is
. The measure of
is given to be
, and the measure of
is given to be
. Therefore, the sum of the measures of the interior angles of pentagon
is
. The interior angle sum theorem applied to pentagon
gives the equation
, which can be solved for
to arrive at
.