Q. 183.7( 19 Votes )

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

Answer :

Given,

*∠**POR and* *∠**ROP* is linear pair

*∠**POR +* *∠**ROP = 180 ^{o}*

Given that,

*∠**POR =* *∠**ROQ = 5: 7*

Therefore,

*∠**POR =* ×* 180 ^{o} = 75^{o}*

Similarly,

*∠**ROQ = 125 ^{o}*

Now,

*∠**POS =* *∠**ROQ = 125 ^{o}*(Vertically opposite angles)

*Therefore,*

*∠**SOQ =* *∠**POR = 75 ^{o}*(Vertically opposite angles)

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