A faster way to do it would be to use the equation for regular polygons:
180(n-2)=total # of angles
where n is the number of sides
And the total number of angles is equal to the number of sides multiplied by the angle of each side (call x the measure of each interior angle, and so it would be xn)
From x + y = 80, you can then figure out that each angle is 140 degrees.
Then just plug into the equation
So there are 9 sides.
I hope that made sense... but yeah equations save so much time lol.