Question

In the adjacent figure the area of trapezium $PQRS$
the opposite angles of a parallelogram are $(7x-12)$ and $(5x+2)$ . Find the measure of each angle.

Answer 1

In a parallelogram, sum of opposite angles is equal

$\begin{array}{c}7x-12=5x+2\\ 7x-5x=2+12\\ 2x=14\\ x=7\\ \angle P=\angle R=7x-12=49-12={37}^0\\ \angle Q=\angle S={180}^0-{37}^0={143}^0\end{array}$