the length of an arc of a circle is 1/5 of its circumference. if the area of the circle is346.5cm²,find the angle subtended by the arc at the centre of the angle​

72°

Step-by-step explanation:

From the question,

Area of the circle = πr²

A = πr² Equation 1

Where r = radius of the circle.

⇒ r = √(A/π) Equation 2

Given: A = 346.5 cm², π = 3.14

r = √(346.5/3.14)

r = √(110.35)

r = 10.5 cm.

Therefore,

circumference of the circle = 2πr = 2×3.14×10.5

circumference = 65.94 m

If the length of the arc(s) is 1/5 of its circumference.

Therefore, length of arc (s) = 13.188

⇒ length of arc/circumference = 13.188/65.94 =  1/5

s/2πr = θ/360

Where θ = angle substends at the center of the circle

1/5 = θ/360

θ = 360/5

θ = 72°