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Explanation & Answer
a) QRST is a kite as opposite angles are not equal so TQ = QR & TS = RS
in triangle TQR , < QTR = < QRT
< QTR = (180 - 102)/2 = 36
in triangle TSR , < STR = < SRT
< STR = ( 180 - 125)/2 = 37.5
< QTS = 36 + 37.5 = 73.5
b) diagonals of kite are perpendicular to each other
TP = PR = TR/2 = 7
QP = 7
in right isoseces triangle QPR
QR^2 = QP^2 + PR^2
= 7^2 + 7^2
QR = 7sq.rt..2
TQ= 7sq.rt.2
PS = QS - QP = 11 - 7 = 4
in right triangle PRS
RS^2 = RP^2 + SP^2 = 7^2 + 4^2
= 65
RS = sq.rt.65
RS = TS = sq.rt.65
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