If the sum of all the interior angles of a regular polygon is 1800 degrees, how many sides does the polygon have?

The sum of all the interior angles of a polygon is given by the formula (n-2) * 180 degrees, where n is the number of sides of the polygon.

In this case, we know that the sum of all the interior angles is 1800 degrees. So we can set up the equation:

(n-2) * 180 = 1800

Solving for n, we get:

n - 2 = 1800 / 180 n - 2 = 10 n = 10 + 2 n = 12

So, the polygon has 12 sides.

Sure, let's solve this step by step.

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

2. Set up the equation: According to the problem, the sum of the interior angles is 1800 degrees. So, we can set up the equation: $(n - 2) \times 180^\circ = 1800^\circ$

3. Solve for $n$: To find $n$, we need to isolate $n$ in the equation. Start by dividing both sides of the equation by 180: $n - 2 = \frac{1800^\circ}{180^\circ}$ Simplify the right-hand side: $n - 2 = 10$

4. Add 2 to both sides to solve for $n$: $n = 10 + 2$ $n = 12$

So, the polygon has 12 sides.