Turn △APB 60 counterclockwise around point A.

Make AB coincide with AC

Similarly, AP also rotates 60 degrees so that point P falls on point Q,

A new △AQC which is congruent with △APB is formed.

∴AQ=AO,PB=QC

In addition, the PC remains unchanged.

∴PQ(=PA)、CQ(=PB)、PC

△ The composition of △PQC is required △

So PA, [B, PC can form delta?

Because ∠ AQC = ∠ APB = 1 13.

So ∠ PQC = ∠ AQC-∠ AQP =113-60 = 53.

Because APC =123.

So ∠ QPC = ∠ APC-∠ APQ =123-60 = 63.

The other angle ∠ pcq = 180-(53+63) = 64.

∴ △PQC Minimum Synthetic Internal Angle = 53.