In a polygon with n sides, half the interior angles are 150 and the other half are 170.find the value of n

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.