How do we find the number of sides of a polygon if we are only given the total sum of the interior angle

Answer 1

set the total sum of the interior angles equal to (n-2)(180) and solve for n

(n-2)(180) where n=# of sides of the polygon is used to find the sum of all of the interior angles

for example, if n=6, then (6-2)(180)=4*180=720 degrees

if n=4, then (4-2)(180)=2*180=360 degrees

suppose the total sum is 1440 degrees

(n-2)(180)=1440

you can divide both sides by 180 or use the distributive property

n-2=8 (dividing)

n=10 sides

180n-360=1440 (distributive property)

180n=1800

n=10 sides