Question

What is the constant of proportionality for the relationship between the length of the arc intercepted by a 80 degree angle and the radius of the circle?

Answer 1

So the length of the arc is given by: l = r*theta, here theta is the intercepted angle in unit radian

So, 80 degrees = 80/360 * 2pi = 4/9 * pi 

So l = r * (4/9 * pi), the constant ratio is 4/9 * pi