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°
