Question

what is the measure of the central angle of a circle with a radius 20 cm that subtends an arc whose length is 35(pi) cm

Answer 1

The measure of the central angle is 315°

Explanation:

The formula of the length of an arc of a circle is L =
`(x)/(360)` × 2πr, where x is the central angle subtended by this arc and r is the radius of the circle

∵ The radius of the circle is 20 cm

∴ r = 20

∵ The length of the arc is 35π cm

∴ L = 35π

- Substitute the values of R and L in the formula above

∵ 35π =
`(x)/(360)` × 2π × 20

∴ 35π =
`(x)/(360)` × 40π

∴ 35π =
`(x)/(9)` π

- Divide both sides by π

∴ 35 =
`(x)/(9)`

- Multiply both sides by 9

∴ 315 = x

∴ The measure of the central angle is 315°