A parallelogram has opposite angles that are congruent so:

\(\displaystyle∠{Q}≅∠{S}\)

\(\displaystyle{m}∠{Q}={m}∠{S}\)

11x+13=15x−23

11x=15x−36

−4x=−36

x=9

So, \(\displaystyle{m}∠{Q}={11}{\left({9}\right)}+{13}={112}°.\)

A parallelogram has consecutive angles that are supplementary:

\(\displaystyle{m}∠{P}+{m}∠{Q}={180}°\)

\(\displaystyle{m}∠{P}+{112}°={180}°\)

\(\displaystyle{m}∠{P}={68}°\)

\(\displaystyle∠{Q}≅∠{S}\)

\(\displaystyle{m}∠{Q}={m}∠{S}\)

11x+13=15x−23

11x=15x−36

−4x=−36

x=9

So, \(\displaystyle{m}∠{Q}={11}{\left({9}\right)}+{13}={112}°.\)

A parallelogram has consecutive angles that are supplementary:

\(\displaystyle{m}∠{P}+{m}∠{Q}={180}°\)

\(\displaystyle{m}∠{P}+{112}°={180}°\)

\(\displaystyle{m}∠{P}={68}°\)