Question

A circle has a circumference of 12. t has an arc of length 8/5. What is the central angle of the arc, in degrees?

Answer 1

Answer:45.9

Explanation:

Circumference=12

Length of arc=8/5=1.6

π=3.14

Circumference=2 x π x r

12=2x3.14xr

12=6.28 x r

Divide both sides by 6.28

12/6.28=(6.28 x r)/6.28

2=r

r=2

Length of arc =Φ/360 x 2 x π x r

1.6=Φ/360 x 2 x 3.14 x 2

1.6=(Φ x 2 x 3.14 x2)/360

1.6=12.56Φ/360

Cross multiply

1.6x360=12.56Φ

576=12.56Φ

Divide both sides by 12.56

576/12.56=12.56Φ/12.56

45.9=Φ

Φ=45.9