Answer:
120°
Step-by-step explanation:
A sector of a circle is the portion or region of a circle enclosed by two radii and an arc. The perimeter of a the sector of a circle is given by the formula:
Perimeter of sector = [tex]\frac{\theta}{360} *2\pi r[/tex] + 2r
Where θ is the angle which forms the sector and r is the radius of the circle.
Given that Perimeter of sector = 57.32 cm, radius (r) = 14 cm, we can find the angle θ using:
Perimeter of sector = [tex]\frac{\theta}{360} *2\pi r[/tex] + 2r
[tex]57.32=\frac{\theta}{360} *2\pi *14+2(14)\\\\57.32-28=\frac{\theta}{360} *2\pi *14\\\\29.32=\frac{\theta}{360} *2\pi *14\\\\ \frac{\theta}{360}=\frac{29.32}{2\pi *14} \\\\\frac{\theta}{360}=0.33\\\\\theta=120^o[/tex]
