Question

if the sum of the measures of the interior angles of a convex polygon is 1440° , how many sides does the polygon have?

Answer 1

S = sum of the interior angles
n = number of sides

S = 1440 is given. Let's solve for n.

S = 180*(n-2)
1440 = 180*(n-2)
1440/180 = 180*(n-2)/180
8 = n-2
8+2 = n-2+2
10 = n
n = 10

There are 10 sides. This is a decagon.