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.

Question

asked Jan 12, 2023 82.3k views

1 Answer

ExternalUse · Answer 1 · 2023-01-16T14:57:33+0000

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,

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