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20 1 1 detailed explanation of the answers to the mathematics test questions in Huanggang senior high school entrance examination.
Solution: Expand BA, do,,,

Let PCD = x,

∫CP sharing ∠ACD,

∴∠ACP=∠PCD=x,PM=PN,

∫BP divided equally ∠ABC,

∴∠ABP=∠PBC,PF=PN,

∴PF=PM,

∫∠BPC = 40,

∴∠ABP=∠PBC=(x-40),

∴∠bac=∠acd-∠abc=2x-(x-40)-(x-40)= 80,

∴∠CAF= 100,

At Rt△PFA and Rt△PMA,

PA=PA,PM=PF,

∴Rt△PFA≌Rt△PMA,

∴∠FAP=∠PAC=50。

So the answer is: 50.