Mikä säännöllinen monikulmio on kyseessä, kun sen kulmien summa on 1440°?

Steps to Solve

1. Use 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:

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

2. Substitute the given sum into the formula

We are given that the sum of the interior angles is $1440^\circ$. So, we substitute $S = 1440^\circ$ into the formula:

$$1440 = (n-2) \times 180$$

3. Solve for $n$

Divide both sides by 180:

$$\frac{1440}{180} = n-2$$

$$8 = n-2$$

Add 2 to both sides:

$$n = 8 + 2$$

$$n = 10$$

4. Identify the polygon

A polygon with 10 sides is called a decagon.