Use the formula for finding the sum of the first nn term of an arithmetic sequence:

\(\displaystyle{S}{n}=\frac{{n}}{{2}}{\left({a}{1}+{a}{2}\right)}\)

\(\displaystyle{S}{n}=\frac{{n}}{{2}}{\left({129}+{159}\right)}\)

PSKSn=144n

The sum of the angles of a convex polygon with nn sides (in degrees) is given by: Sn=180(n−2)

Equating (1) and (2), we solve for nn: 144n=180(n−2)

144n=180n−360

−36n=−360

n=10

So, the convex polygon has 10 sides.