# In Fig. 8.47, lines PQ and RS intersect each other at point O. If ∠POR : ∠ROQ = 5 : 7, find all the angles.

Given,

POR and ROP is linear pair

POR + ROP = 180o

Given that,

POR = ROQ = 5: 7

Therefore,

POR =  × 180o = 75o

Similarly,

ROQ = 125o

Now,

POS = ROQ = 125o(Vertically opposite angles)

Therefore,

SOQ = POR = 75o(Vertically opposite angles)

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