If equilateral polygon penta is inscribed in a circle of radius 15 inches so that all of its vertices are on the circle, what is the length of the shorter arc from vertex p to vertex n?

The shorter arc from p to n covers 2/5 of the circumference (the longer arc would cover 3/5 of it).
The circumference is calculated using the formula 2*pi*r
= 2*pi*(15 inches)
= 30*pi inches
So the length of the arc is (2/5) * (circumference)
= (2/5) * (30*pi)
= 12*pi inches.