Total number of sides = n
Half, means n/2 of them have 150° each.
Half, means n/2 of them have 170° each.
Sum of angles in a polygon is given by the formula: (n -2)*180.
So summing the first of 150 degrees and the other half of 170 would be equal to the total of (n -2)*180.
(n/2)*150 + (n/2)*170 = (n -2)*180
(n/2)*(150 + 170) = (n -2)*180
(n/2)*(320) = (n -2)*180
160n = 180n - 360
160n - 180n = -360
-20n = -360
n = (-360) / (-20). Divide out
n = 18
So the polygon has 18 sides.
I hope this helps.
Regards.
