Question

lines PQ and RS intersect each other at ooint o if angel POR: angle ROQ = 5:7 then find all the remaining angles

Answer 1

consider angle POR as 5x and and ROQ as 7x,
so POR and ROQ lie on the same plane thus, POR+ROQ= 180 degrees.
therefore. 5x+7x=180
              12x=180
                x= 180/12
                  =15
              => 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]

Answer 2

POR = 5x ROQ = 7x . . . PQ and RS intersect at each other soPOR and ROQ are linear pair therefore POR+ROQ =5x+7x=180 12x. = 180 X. = 180/12 X. =15 5x =5×15=75° 7x = 7×15= 105° 7x=105°; 5x=75°