Consider angle POR as 5x and and ROQ as 7x,
so POR and ROQ lie on the same plane thus, POR+ROQ= 180 degrees.
=> 5x- 5*15 =75 and 7x-7*x=105
now, POS is also 105 degrees as ROQ and POS are interior alternate angles and SOQ is also 75 degrees as POR ans SOQ are interior alternate angle..
[if you have any more doubts,do ask me as this is my fav. concept of math]