Question

If the radius is 14cmand The perimeter of the sector is 57.32cm.what is the size of the angle?​

Answer 1

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 = $\frac{\theta}{360} *2\pi r$ + 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 = $\frac{\theta}{360} *2\pi r$ + 2r

$57.32=\frac{\theta}{360} *2\pi *14+2(14)\\\\57.32-28=\frac{\theta}{360} *2\pi *14\\\\29.32=\frac{\theta}{360} *2\pi *14\\\\ \frac{\theta}{360}=\frac{29.32}{2\pi *14} \\\\\frac{\theta}{360}=0.33\\\\\theta=120^o$