解?$：(2)$?∵?$BP⊥CP，$?
∴?$∠BPC=90°，$?
∴?$∠PBC+∠PCB=90°$?
∵?$BP，CP{分別是}∠ABC$?的?$“$?鄰?$AB$?三分線?$”$?和?$∠ACB$?的?$“$?鄰?$AC$?三分線?$”$?
∴?$∠PBC=\frac {2}{3}∠ABC，∠PCB=\frac {2}{3}∠ACB$?
∴?$\frac {2}{3}∠ABC+\frac {2}{3}∠ACB=90°$?
∴?$∠ABC+∠ACB=135°$?
∴?$∠A=180°-(∠ABC+∠ACB)=180°-135°=45°$?
