Answer
$41.6^\circ, 138.4^\circ$
Work Step by Step
Use the Law of Sines, we have $\frac{sinA}{a}=\frac{sinC}{c}\longrightarrow \frac{sinA}{534}=\frac{sin25.4^\circ}{345}\longrightarrow sinA\approx0.6639$. As angle $A\in[0,\pi]$, we have $A=asin(0.6639)=41.6^\circ\ and\ 138.4^\circ$
