Answer:
The measure of the central angle is 315°
Step-by-step explanation:
The formula of the length of an arc of a circle is L = [tex]\frac{x}{360}[/tex] × 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 = [tex]\frac{x}{360}[/tex] × 2π × 20
∴ 35π = [tex]\frac{x}{360}[/tex] × 40π
∴ 35π = [tex]\frac{x}{9}[/tex] π
- Divide both sides by π
∴ 35 = [tex]\frac{x}{9}[/tex]
- Multiply both sides by 9
∴ 315 = x
∴ The measure of the central angle is 315°
