How does (-13π)/3 rad =-780°?

${180}^{\circ} \equiv \pi$
So, whatever you do to $\pi$ you do to ${180}^{\circ}$
Therefore, to go from radians to degrees, you multiply by $\frac{180}{\pi}$
$- \frac{13 {\pi}^{c}}{3} \cdot \frac{180}{\pi} \equiv - {780}^{\circ}$