Answer
$A= 40^\circ$
$a =2$
$c\approx3.06$
Work Step by Step
Step 1. Using the given figure and conditions, we have $A=180-100-40=40^\circ$
Step 2. Using the Law of Sines, we have $\frac{a}{sin40^\circ}=\frac{c}{sin100^\circ}=\frac{2}{sin40^\circ}$
Step 3. Thus $a=\frac{2sin40^\circ}{sin40^\circ}=2$ and $c=\frac{2sin100^\circ}{sin40^\circ}\approx3.06$
