Two problems in junior high school mathematics → Solving problems by using axial symmetry ← Solving problems quickly means solving problems quickly!

C is the vertical line CD of AP, and the vertical foot is point D, connected to BD;

∫△PCD，∠APC=60？ ,

∴∠DCP=30？，PC=2PD，

PC = 2PB，

∴BP=PD，

△ BPD is an isosceles triangle, △ BDP = △ DBP = 30? ,

∫∠ABP = 45？ ,

∴∠ABD= 15？ ,

∠∠BAP =∠APC？ ∠ABC=6045？ = 15?

∴∠ABD=∠BAD= 15？ ,

∴BD=AD，

∵∠DBP=45 15？ =30? ，∠DCP=30？ ,

∴BD=DC，

△ BDC is an isosceles triangle,

BD = AD，

∴AD=DC，

∫∠CDA = 90？ ,

∴∠ACD=45？ ,

∴∠ACB=∠DCP+∠ACD=75？ ,

So the answer is: 75.

I hope I can help you?

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