If the ratio of the number of sides of a polygon to the number of diagonals is$\text{2}:\text{5}$ , then the sum of the angles of the polygon is

d $\to$ number of diagonals  and $d=\frac{n\left(n-3\right)}{2}$

$n:d=2:5$        

$\Rightarrow \frac{n}{d}=\frac{2}{5}$        

$\Rightarrow \frac{2}{n-3}=\frac{2}{5}$

$\Rightarrow \frac{n}{n\left(\frac{n-3}{2}\right)}=\frac{2}{5}$

$\Rightarrow n-3=5$

$n=8$

Sum of interior angles $=\left(n-2\right)180°$

$=6\times 180°$

$=1080°$