Given an arc of a sector is three times its radius, find the angle subtended by

the arc.

The angle subtended by the arc is 171.8873385 degrees (3 radians)

Step-by-step explanation:

The formula of the length of an arc of a sector is L = × 2 π r, where

∵ An arc of a sector is three times its radius

∴ L = 3r

→ Equate the formula of the length of the arc by 3r

∵ × 2 π r = 3r

→ Divide both sides by r

∴   × 2 π = 3

→ Simplify the left side

∵   x = 3

→ Divide both sides by  

∴ x = 171.8873385°

∴ The angle subtended by the arc is 171.8873385 degrees (3 radians)

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.