2. Number of sides for a polygon with a sum of $$ 8640^{\circ} $$ for the interior angles

Question

UpStudy AI · Accepted Answer

We start with the formula for the sum of the interior angles of an $$ n $$-sided polygon:

$$
(n-2) \times 180^\circ = \text{Sum of interior angles}
$$

Given that the sum of the interior angles is $$ 8640^\circ $$, we have:

$$
(n-2) \times 180^\circ = 8640^\circ
$$

**Step 1: Solve for $$ n-2 $$**

Divide both sides by $$ 180^\circ $$:

$$
n-2 = \frac{8640}{180}
$$

$$
n-2 = 48
$$

**Step 2: Solve for $$ n $$**

Add $$ 2 $$ to both sides:

$$
n = 48 + 2 = 50
$$

Thus, the polygon has $$ 50 $$ sides.
The polygon has 50 sides.

Number of sides for a polygon with
a sum of for the interior angles