Answer
$C= 100^\circ$
$a \approx 1.31$
$b \approx 1.31$
Work Step by Step
Step 1. Using the given conditions, we have $C=180-40-40=100^\circ$
Step 2. Using the Law of Sines, we have $\frac{a}{sin40^\circ}=\frac{b}{sin40^\circ}=\frac{2}{sin100^\circ}$
Step 3. Thus $a=\frac{2sin40^\circ}{sin100^\circ} \approx 1.31$ and $b=\frac{2sin40^\circ}{sin100^\circ}\approx 1.31$