Final answer:
To find the central angle of a sector with a given area and radius, the formula for the area of the sector is used, and 57.3 degrees is the calculated angle. However, the provided options do not match this value exactly.
Step-by-step explanation:
The question asks to find the measure of the central angle of a sector in a circle, given the area of the sector is 15 cm² and the radius of the circle is 6 cm. To find the angle, we can use the formula for the area of a sector of a circle, which is (angle/360)×(π×radius²). Plugging in the known values, we have (angle/360)×(π×(6 cm)²) = 15 cm². To solve for the angle, we first calculate (π×(6 cm)²) and then rearrange the equation to solve for the angle.
Solving this, the angle is approximately 57.3 degrees. This angle doesn't match exactly with any of the options provided, but if we're rounding to the nearest degree, the closest option is option a) 45°. As the closest option given is lower than the calculated angle, which falls closer to 60°, it is important to clarify that there might be a typo in the options or in the calculation process.