Question

In a parallelogram PQRS, if angle P = (2x+25) degrees and angle Q = (3x-5) degrees, then write the measures of angle S and angle R.

Answer 1

Consecutive angles of a parallelogram are supplementary, so:

$2x+25+3x-5=180\\5x+20=180\\5x=160\\x=32$

This means $m\angle P=2(32)+25=89^{\circ}$ and that $m\angle Q=3(32)-5=91^{\circ}$.

Since opposite angles of a parallelogram are congruent,

$\boxed{m\angle S=91^{\circ}, m \angle R=89^{\circ}}$