To determine the number of sides of a convex polygon given that the sum of its interior angles is 1800°, follow these steps:
1. Recall the formula for the sum of the interior angles of a polygon:
The sum of the interior angles of a polygon with [tex]\( n \)[/tex] sides can be calculated using the formula:
[tex]\[
\text{Sum of interior angles} = (n - 2) \times 180^\circ
\][/tex]
where [tex]\( n \)[/tex] is the number of sides of the polygon.
2. Set up the equation:
We are given that the sum of the interior angles is 1800°. So, plug the given sum into the formula:
[tex]\[
(n - 2) \times 180 = 1800
\][/tex]
3. Solve for [tex]\( n \)[/tex]:
To find the number of sides [tex]\( n \)[/tex], we need to solve the equation for [tex]\( n \)[/tex].
[tex]\[
(n - 2) \times 180 = 1800
\][/tex]
Divide both sides of the equation by 180 to isolate [tex]\( n - 2 \)[/tex]:
[tex]\[
n - 2 = \frac{1800}{180}
\][/tex]
4. Simplify the right-hand side:
[tex]\[
n - 2 = 10
\][/tex]
5. Solve for [tex]\( n \)[/tex] by adding 2 to both sides:
[tex]\[
n = 10 + 2
\][/tex]
[tex]\[
n = 12
\][/tex]
Therefore, the convex polygon with an interior angle sum of 1800° has [tex]\(\boxed{12}\)[/tex] sides.
