This is an interesting problem from the Canadian Mathematical Society’s 2001 Olymon.
“Suppose that XTY is a straight line and that TU and TV are two rays emanating from T for which XTU = UTV = VTY = 60º. Suppose that P, Q and R are respective points on the rays TY, TU and TV for which PQ = PR. Prove that QPR = 60º.”
See the Ubiquitous 60 Degree Problem