Question

if each interior angle of a regular polygon measures 144 degrees, how many sides does the polygon have?

Answer 1

so what do you think angle "x"?

Answer 2

Polygon angles = (number of sides -2) * 180
So triangle has 180° total
square = 360°

Now the measure of EACH angle is given by
"Average" angle = [(number of sides -2) * 180] / number of sides
so for 144° we have
144° = [(number of sides -2) * 180] / number of sides
number of sides = # sides-2 * 180 / 144
(number of sides / number of sides-2) = 180 / 144

I managed to work up this formula but haven't been able to get beyond the
"(number of sides / number of sides-2)" step

Answer 3

(number of sides / number of sides-2) = 180 / 144
Dividing top and bottom of (180/44) by 36
(number of sides / number of sides-2) = 5 / 4
(n / n-2) = 5 / 4
n = (5n -10) / 4
(5n -10) / n = 4
multiplying both sides by n
5n - 10 = 4 * n
5n -4n = 10
n = 10