Area of sectors

Question

The diameter of a circle is 10 kilometers. What is the angle measure of an arc bounding a sector with area 10​𝜋 square kilometers? Give the exact answer in simplest form.

Answer 1

If d, the diameter of the circle, is 10, then, d/2, the radius, r, of the circle is 5, which means that the area of the circle is 25𝜋, which means that the area of a sector of 10𝜋 would be 2/5 of the that of the circle. 2/5 of 360 degrees is 72 X 2 = 144 degrees.