Answer
$C=50{}^\circ,a\approx 7.1$ and $b\approx 7.1$.
Work Step by Step
First we will find the value of C.
Properties of a triangle:
The sum of three angles is $A+B+C=180{}^\circ $
$\begin{align}
& A+B+C=180{}^\circ \\
& 65{}^\circ +65{}^\circ +C=180{}^\circ \\
& C=180{}^\circ -130{}^\circ \\
& C=50{}^\circ
\end{align}$
Now, we will find the remaining sides using the ratio
$\frac{c}{\sin C}$,or $\frac{6}{\sin 50{}^\circ }$,
Now, we will use the law of sines to find a.
$\begin{align}
& \frac{a}{\sin A}=\frac{c}{\sin C} \\
& \frac{a}{\sin 65{}^\circ }=\frac{6}{\sin 50{}^\circ } \\
& a=\frac{6\sin 65{}^\circ }{\sin 50{}^\circ } \\
& a\approx 7.1
\end{align}$
Using the law of sines again, we will find b.
$\begin{align}
& \frac{b}{\sin B}=\frac{c}{\sin C} \\
& \frac{b}{\sin 65{}^\circ }=\frac{6}{\sin 50{}^\circ } \\
& b=\frac{6\sin 65{}^\circ }{\sin 50{}^\circ } \\
& b\approx 7.1
\end{align}$
