The degree measure of the arc is the central angle of the circle
The degree measure of the arc is 90 degrees
How to calculate the degree measure of the arc
The area (a) of the sector is 36π and the area (A) of the circle is 144π.
The area of a sector is calculated as:
[tex]a = \frac{\theta}{360} * A[/tex]
So, we have:
[tex]36\pi = \frac{\theta}{360} * 144\pi[/tex]
Divide both sides by [tex]36\pi[/tex]
[tex]1 = \frac{\theta}{360} * 4[/tex]
Evaluate the product
[tex]1 = \frac{\theta}{90}[/tex]
Solve for [tex]\theta[/tex]
[tex]\theta = 90[/tex]
Hence, the degree measure of the arc is 90 degrees
Read more about sectors and circles at:
https://brainly.com/question/16736105
