Question

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

Answer 1

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

Answer 2

\[360=180n-144n=36n\]Dividing both sides by 36 gives \[n=10\]

Answer 3

You have a decagon.

Answer 4

thank you