Question

line PQ and Rs intersect each other at point O if angle p o r : angle :r o q is equal to 5 :7 find all the angles

Answer 1

Let ∠POR = 5x and ∠ROQ = 7x

Now,

 ∠POR + ∠ROQ = 1800  (Angles on the same line)

5x + 7x = 180

12x =180

x= 150

Therefore, ∠POR = 750 and ∠ROQ = 1050

Now,

∠POR = ∠SOQ  (Vertically opposite angles)

∠ROQ = ∠POS  (Vertically opposite angles)

Therefore, ∠SOQ = 750  and ∠POS = 1050

hope it's helps you

Answer 2

Let angle por be 5x
and angle roq be 7x
so, 5x+7x=180. (linear pair angles)
=>12x=180
=>x=180/12
=>x=15
so, 5x=5(15)=75
7x=7(15)=105
so, angle por=angle soq=75
and, angle roq=angle pos=105.