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)}`