A quadrilateral's angles are in the ratio $3:6:8:13$. Then find the greatest angle.

Let's assume, 

$\angle \mathrm{A}=3\mathrm{x}, \angle \mathrm{B}=6\mathrm{x},\angle \mathrm{C}=8\mathrm{x},\angle \mathrm{D}=13\mathrm{x}$.

According to the angle sum property of a quadrilateral $\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}+\angle \mathrm{D}=360°$

$3\mathrm{x}+6\mathrm{x}+8\mathrm{x}+13\mathrm{x}=360°$

$30\mathrm{x}=360°$

$\mathrm{x}=\frac{360°}{30}=12°$

$\angle \mathrm{A}=3\mathrm{x}=3\times 12°=36°$ 

$\angle \mathrm{B}=6\mathrm{x} =6\times 12°=72°$

$\angle \mathrm{C}=8\mathrm{x}=8\times 12°=96°$

$\angle \mathrm{D}=13\mathrm{x}=13\times 12°=156°$

Therefore, the greatest angle is $\angle \mathrm{D}=156°$.