We are given the figure of an circle inscribed with a triangle with the following values:
arc SN = 60 degrees
arc QS = x
arc QP = x + 40
arc PN = 2x - 16
To solve for the values of the arcs, we need to find x:
arc SN = angle 2 = 60 degrees
angle 2 is supplementary with angle 6
angle 6 = arc PN = 2x - 16 = 180 - 60 degrees
so,
2x - 16 = 120
solve for x:
x = 68 degrees
substitute x for the rest of the unknown values and now you have your complete set of values for the figure.