Problem: If the sum of the measures in degrees of angles , and in the figure to the right is , then is equal to
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let and denote the intersectiong of with and reapectively. Then sums of angles in degrees are
\angle F+\angle F P D+\angle E Q A+\angle E=360^
\angle B+\left(180^{\circ}-\angle F P D\right)+\angle D=180^
\angle A+\left(180^{\circ}-\angle E Q A\right)+\angle C=180^
Adding these equation member by member cives
and the required sum is that as in choice (C).
