Question 928312
Since P and Q are adjacent vertices, the angles are supplementary, so they add up to {{{180^o}}} :
{{{(3x-4)+(5x+8)=180}}}
{{{3x-4+5x+8=180}}}
{{{8x+4=180}}}
{{{8x=180-4}}}
{{{8x=176}}}
{{{x=176/8}}}
{{{x=22}}}
Then,
{{{3x-4=3*22-4}}}--->{{{3x+4=66-4}}}--->{{{3x-4=62}}}
Angle P measures {{{62^o}}} , and so does the opposite angle, R.
Angles Q and S measure {{{180^o-62^o=118^o}}}
As a verification, we could calculate
{{{5x+8=5*22+8}}}--->{{{5x+8=110+8}}}--->{{{5x+8=118}}}