$\overline{CX} = \overline{CB}  \to \hat{X}=\hat{B}$  $\overline{AX} = \overline{CX}  \to \hat{A}=\hat{C}$ $\hat{X1}=180-\hat{X} \to \hat{X1}=\hat{B}+\hat{C}=\hat{X}+\hat{A} \to 180-\hat{X}=\hat{X}+\hat{A} \to \hat{X}=90-\frac{\hat{A}}{2}$ $\hat{X1}=180-\hat{X}=180-(90-\frac{\hat{A}}{2})=90+\frac{\hat{A}}{2}$ $\hat{A}+\hat{C}+\hat{X1}=180 \to \hat{A}+\hat{A}+90+\frac{\hat{A}}{2}=180$ $\hat{A}+\hat{A}+90+\frac{\hat{A}}{2}=180 \to \frac{5}{2}\hat{A}= 180 \to \hat{A}=36$