anonymous 5 years ago The measure of each interior angle of a regular polygon is 144 degrees. How many sides does the polygon have?

1. anonymous

Regular polygon is by DEFINITION a convex polygon that has ALL internal angles and ALL sides equal. You only need the fact that all internal angles are equal. I said in another answer that the sum of the internal angles of ANY convex polygon is (n-2)*180 degrees. So$144n=(n-2)180\rightarrow144n=180n-360$Solve for n to get

2. anonymous

$360=180n-144n=36n$Dividing both sides by 36 gives $n=10$

3. anonymous

You have a decagon.

4. anonymous

thank you