The radius of a circle is 15 feet. what is the angle measure of an arc bounding a sector with area 15 square feet

You have to use the formula for the area of a sector here to get your angle.  The angle measure you're looking for, the central angle measure, is the same measure as its intercepted arc.  That formula is .  Here's what we are given to fill in: which simplifies to .  You could multiply both sides by 360 then divide by 225pi to get that the angle measure is 7.6 degrees, which seems about right when you think about it since the area of the sector bounded by that arc is only 15.

The first option would be correct if it were one half and not one