Question

What is the measure of the central angle indicated in red in degrees?
6
1/3

Answer 1

Answer: The measure of the central angle indicated in red is 20°

Explanation:

We know that a circle subtends an angle of 360° at the centre.

In other words, the circumference of length 6 subtends an angle of 360°, and similarly, we have to find out the angle that length
`(1)/(3)` subtends at the centre.

By rule of direct proportion:

if 6→360° Then,

`(1)/(3)` →x°

Cross multiplying

`6x=360*(1)/(3)`

`x=20`

The general formula for calculating any angle subtended by an arc of length x:
`(2*\pi*x )/(c)`

where x is the given length of arc and c is the circumference.