Question

A circle has a circumference of 8. It has an arc of length 32/5.

What is the central angle of the arc, in degrees?

Answer 1

288°

Explanation:

`l = ( \theta)/(360 \degree) * c \\ \\ where \\ l = length \: of \: the \: arc \\ \theta \: = measure \: of \: the \: central \: angle \\ c = circumference \: of \: the \: circle \\ \\ \implies \: (32)/(5) = ( \theta)/(360 \degree) * 8 \\ \\ 40 \theta = 32 * 360 \degree \\ \\ \theta = ( 32 * 360 \degree)/(40) \\ \\ \theta =32 * 9 \degree\\ \\ \theta =288 \degree`