The sum of the interior angles of a regular polygon is six times the sum of its exterior angles. Determine the number of diagonals in the polygon.

Let the number of sides of the polygon be = n
Sum of interior angles =(n-2)$ \times180^\circ$
Sum of exterior angles =$ 360^\circ$
Given: (n-2) $ \times180=6\times360$
(n-2) $ \times180=2160$
n-2=12 = n=14
Number of diagonals = $ \frac{n(n-3)}{2}=\frac{14(14-3)}{2}=77$