A circle has a circumference of 20. It has an arc of length 4. What is the central angle of the arc, in degrees

Step-by-step explanation: 72.1°

The circumference of the circle is given to be = 20

The first thing to do here is to calculate the radius of the circle from the circumference given,

Formula for circumference = 2πr or πd, where d is the diameter.

Make r the subject of the formula by equating it to 20

2πr = 20,

r = 20/2π, π = ²²/₇ or 3.142

r = 10/22/7

= (10 x 7) / 22

= 70/22

= 3.18.

Now since the radius is known, we could now calculate the central angle of the arc.

Arc length = 2πr∅°/360°, reducing this to lowest term now becomes

= πr∅°/180°

Therefore equate the formula to 4 and solve for ∅°, since the arc length is 4

πr∅°/180° = 4

Multiply through by 180°

πr∅° = 4 x 180°

πr∅° = 720

Divide through by πr to get ∅°

∅° = 720/πr

= 720/3.142 x 3.18

= 720/9.99

= 72.07

= 72.1°

The angle substended by the arc length 4 is 72.1°