If the sum of the measures of all the interior angles of a polygon is 1800
∘
, find the number of sides of the polygon.

The formula for the sum of the interior angles of an n-sided polygon is:
Sum=(n−2)×180
∘

Given that the sum is 1800
∘
:

(n−2)×180
∘
=1800
∘

Divide both sides by 180
∘
:

n−2=
180
1800
​

n−2=10
n=12
Therefore, the polygon has 12 sides.