$\overline{CP} = \overline{CB}  \to \hat{P}=\hat{B}$  $\overline{AP} = \overline{CP}  \to \hat{A}=\hat{C}$ $\hat{P1}=180-\hat{P} \to \hat{P1}=\hat{B}+\hat{C}=\hat{P}+\hat{A} \to 180-\hat{P}=\hat{P}+\hat{A} \to \hat{P}=90-\frac{\hat{A}}{2}$ $\hat{P1}=180-\hat{P}=180-(90-\frac{\hat{A}}{2})=90+\frac{\hat{A}}{2}$ $\hat{A}+\hat{C}+\hat{P1}=180 \to \hat{A}+\hat{A}+90+\frac{\hat{A}}{2}=180$ $\hat{A}+\hat{A}+90+\frac{\hat{A}}{2}=180 \to \frac{5}{2}\hat{A}= 180 \to \hat{A}=36$