PQRS is a square and SRT is an equilateral triangle. Prove that PT=QT and angle TQR=15 degrees
consider triangle PST and triangle QRT
PS = QR (side of a square)
TS = TR (sides of an equilateral triangle)
angle PST = angle QRT = 150 degrees ( 90 degrees + 60 degrees)
therefore SAS congruency triangle PST is congruent triangle QRT
PT = QT ((c.p.c.t.)
now, QR = RS
and RS = RT
so, QR = TR
this implies that, angle RTQ = angle RQT
angle RTQ + angle RQT + 150 degree = 180 degrees
2 angle RQT = 30 degrees
therefore angle RQT = 15 degrees