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In quadrilateral PQRS, the bisector of angle R and S meet at point T, show that Anlge P + Angle Q = 2 AngleRTS.

In quadrilateral PQRS, the bisector of angle R and S meet at point T, show that Anlge P + Angle Q = 2 AngleRTS. 
 

Grade:10

1 Answers

rohit
23 Points
6 years ago
in triangle TSR:-
angleTSR=s/2,angleSRT=R/2.
sum of angles in triangle TSR=180
so, TSR+SRT+RTS=180
so,S/2+R/2+RTS=180
so,RTS=180-(S/2+R/2)..........................................................(1)
in quad. PQRS,sum of angles=360
so, P+Q+R+S=360
so,P+Q=360-(R+S)
so,P+Q=2{180-(R/2+S/2)}
so,P+Q=2{angleRTS}..................................[from (1)]
 
cheers!
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