Answer:
When we have a circle of radius R, we have that the total perimeter of the circle is equal to:
P = 2*pi*R
Now, if we have an arc, this is only a section of the total perimeter, the measure of the arc is equal to:
A = (θ/2*pi)*2*pi*R = θ*R
You can see that when θ = 2*pi, the term in the left is equal to 1 and we have the complete perimeter.
Now, we have that the measure of the arc AB = 72, then we can find the angle as:
A = 72 = θ*R
then we solve this for theta:
72/R = θ
Where you can see that as bigger is the radius of the circle, smaller is the value of theta.
Remember that this equation works with angles in radians.
