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 .