Answer:
120°
Step-by-step explanation:
The area of a sector of a circle is given by:
[tex]A = \frac{\alpha }{360} * \pi r^2[/tex]
where α = central angle of sector in degrees
r = radius of circle.
The radius of the circle is 15 cm and the area of the sector is 235.62 cm^2. Therefore:
[tex]235.62 = \frac{\alpha }{360} * \pi * 15^2\\\\84823.2 = 706.86 * \alpha \\\\=> \alpha = 84823.2 / 706.86\\\\\alpha = 120^o[/tex]
The central angle of the sector is 120°
