Question

if arc BC=63 how do I calculate the measurment of angle BPC

Answer 1

The angle we are talking about is the one that originates at the big bold dot correct?

Answer 2

correct

Answer 3

(angle projected at the center of circle/arc length)=(360°/circumference of circle)
This is the formula required. All you need to do is find the circumference (or radius) of the circle.