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 .