Question

the quadrilateral PQRS , the bisector of angle R and angle S meet a print T. show that angle p +angle Q =2 angle RTS​

Answer 1

Answer:

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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