It can be seen from the meaning of the question that △APB is all equal to △ AP 'c

So ∠PAB=∠P'AC

So ∠ PAP' = ∠ PAC+∠ CAP' = PAC+∠ PAB = ∠ BAC = 60.

So △APP' is a regular triangle, so PP'=3.

Because P'C=PB=4.

PC=5

So ∠ PP 'c = 90.

So ∠ APB = ∠ AP 'c = 90+60 = 150.

The last two questions are incomplete. Please check the problem again.