The measures of the angles of a triangle are in the ratio 5:6:7. What is the number of degrees in the largest of these angles?
Since the angle measures are in the ratio $5:6:7$, the measures are $5x$, $6x$, and $7x$ for some value of $x$.  Since these are the angles of a triangle, we have $5x+6x+7x = 180^\circ$, so $18x = 180^\circ$ and $x = 10^\circ$.  Therefore, the largest angle is $7x = \boxed{70^\circ}$.