in quardilateral pqrs , the bisector angle. p and angle q meet at o. prove angle poq=1/2 of angle r + angle s
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To Prove: <POQ=1/2 (<R+<S)
Proof:<P+<Q+<R+<S=360°
<P+<Q=360°-<R-<S
2x+2y=360°-<R-<S
x+y+<POQ= 180°[ASP]
2x+2y+2 <POQ=360°--------1
2x+2y+<R+<S=360°-------2
Substituting, eqn (1)&(2),
2x+2y+2 <POQ=2x+2y+<R +<S
2 <POQ=<R+<S
<POQ=1/2 (<R+<S)
Hope it may help you....
Proof:<P+<Q+<R+<S=360°
<P+<Q=360°-<R-<S
2x+2y=360°-<R-<S
x+y+<POQ= 180°[ASP]
2x+2y+2 <POQ=360°--------1
2x+2y+<R+<S=360°-------2
Substituting, eqn (1)&(2),
2x+2y+2 <POQ=2x+2y+<R +<S
2 <POQ=<R+<S
<POQ=1/2 (<R+<S)
Hope it may help you....
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