The angles of a quadrilateral are in the ratio 3:5:9:13. Find the measure of the largest angle.

Let the angles be $3x, 5x, 9x,$ and $13x$. The sum of angles in a quadrilateral is $360^\circ$. So, $3x + 5x + 9x + 13x = 360^\circ \implies 30x = 360^\circ \implies x = 12^\circ$. The largest angle is $13x = 13 \times 12^\circ = 156^\circ$.