Question

Consider the circle with a 4 centimeter radius. If the length of major arc RT is

64/9π, what is the measure of ∠RST?
a.20
b.25
c.30
d.40

Answer 1

Answer: 20

Explanation:

Click link below for explanation.

Good Luck!

Answer 2

Option D is correct.i.e., ∠ RST = 40°

Explanation:

Given: Radius of circle, r = 4 cm

Center of circle is S and Length of Major ARC RT =
`(64)/(9)*\pi`

To find: ∠ RST

Figure is attached

Let
`\theta` be the ∠ RST.

we use the formula of Length of Arc,

`Length\: of\: Arc\: =\:(\theta)/(360^(\circ))*2\pi r`

We use this formula to find the angle made by arc RT at centre S,

`Length\:of\:major\:Arc\:=\:(360^(\circ)-\theta)/(360^(\circ))*2\pi r`

`(64)/(9)*\pi=\:(360^(\circ)-\theta)/(360^(\circ))*2\pi *4`

`(64)/(9)*\pi=\:(360^(\circ)-\theta)/(360^(\circ))*8\pi`

`(360^(\circ)-\theta)/(360^(\circ))=(64*\pi)/(9*8\pi)`

`(360^(\circ)-\theta)/(360^(\circ))=(8)/(9)`

`360^(\circ)-\theta=(8*360)/(9)`

`360^(\circ)-\theta=8*40`

`360^(\circ)-\theta=320`

`-\theta=320-360`

`-\theta=-40`

`\theta=40`

Therefore, Option D is correct.i.e., ∠ RST = 40°