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