If the sum of the measures of all the interior angles of a polygon is 1440
∘
, find the number of sides of the polygon.

The sum of the interior angles of a polygon with n sides is given by the formula:
Sum=(n−2)×180
∘

Given that the sum is 1440
∘
:

(n−2)×180
∘
=1440
∘

n−2=
180
1440
​

n−2=8
n=8+2=10
Thus, the number of sides of the polygon is 10.