Find the number of diagonals of a regular polygon, the sum of whose interior angles is $2700^\circ$.

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**Solution:**

1. Let the number of sides of the regular polygon be *n*.

2. The sum of interior angles of a polygon is given by:
   $$\text{Sum of interior angles} = (n - 2) \times 180^\circ$$

3. Given the sum of interior angles is $2700^\circ$, so:
   $$2700 = (n - 2) \times 180$$

4. Solve for *n*:
   $$
   n - 2 = \frac{2700}{180} = 15 \
   n = 15 + 2 = 17
   $$

5. The number of diagonals in a polygon with *n* sides is:
   $$\frac{n \times (n - 3)}{2}$$

6. Substitute *n = 17*:
   $$
   \frac{17 \times (17 - 3)}{2} = \frac{17 \times 14}{2} = \frac{238}{2} = 119
   $$

**Answer:** 119

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