Question

in quadrilateral PQRS the bistector of angle R and angle S meets at point T . show that angle P + angle Q =2 angle RTS

Answer 1

Answer:
                We have a quadrilateral PQRS , where bisectors of angle R and angle S meet at point T.
                                 
We know in quadrilateral,
             ∠ P + ∠Q + ∠R + ∠S = 360°
               ∠ P + ∠Q =  360° - (∠R + ∠S)          --------------- (1)         

In ∆RTS ,
         ∠RTS + ∠TSR  + ∠SRT = 180°             ---------------  (2)
 Given,
         ∠TSR    = ∠S/2
          ∠SRT  = ∠R/2
         After substitute this in  equation (2) , we get

         ∠RTS + ∠S/2 +∠R/2 =  180° 
     ⇒ 2∠RTS  +∠S  +∠R   = 360°
    ⇒  2∠RTS = 360° - (∠R + ∠S)
From equation number (1)
     ⇒ 2∠RTS =   ∠ P + ∠Q                                         (Hence proved)


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Answer 2

Answer:

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