Question

CAN SOMEONE PLEASE PLEASE HELP ME ON THIS IM DESPERATE

Answer 1

The angle has a measure of
`(5\pi)/(6)` radians.

Explanation:

According to the statement, an angle centered at the center of the circle covers an arc of
`(25\pi)/(6)` units, the arc is a portion of the circunference. We include a figure representing the circle below.

Where:

`R` - Radius, measured in units.

`s` - Arc, measured in units.

`\alpha` - Angle of the arc, measured in radians.

From Geometry, we can calculate the length of the arc by means of this equation:

`s = \alpha\cdot R` (1)

If we know that
`R = 5` and
`s = (25\pi)/(6)`, then the angle of the arc is:

`\alpha = (s)/(R)`

`\alpha = ((25\pi)/(6) )/(5)`

`\alpha = (25\pi)/(30)`

`\alpha = (5\pi)/(6)\,rad`

The angle has a measure of
`(5\pi)/(6)` radians.