Question

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

Answer 1

Answer:

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°