#### Answer

The two possible values for angle $A$ are $41.6^{\circ}$ and $138.4^{\circ}$

#### Work Step by Step

We can use the law of sines to find the angle $A$:
$\frac{c}{sin~C} = \frac{a}{sin~A}$
$sin~A = \frac{a~sin~C}{c}$
$sin~A = \frac{(534)~sin~(25.4^{\circ})}{345}$
$A = arcsin(0.6639)$
$A = 41.6^{\circ}$
Note that we can also find another value for the angle A:
$A = 180^{\circ}-41.6^{\circ} = 138.4^{\circ}$
The two possible values for angle $A$ are $41.6^{\circ}$ and $138.4^{\circ}$