We can do it with the equation written; we'll try that next. I find it easier to remember the exterior angles, which are the supplements of the interior angles, add to 360 degrees.
The exterior angle is 180 - 144 = 36 degrees. n = 360/36 = 10
Answer: 10 sides
Let's try it your way now.
[tex]\dfrac{180(n-2)}{n} = 144[/tex]
[tex]180n-360 = 144 n[/tex]
[tex]36n = 360[/tex]
[tex]n = 10 \qquad\checkmark[/tex]
