Question

Major arc CBD measures 300°. Which is the radian measure of its corresponding central angle? radians radians radians radians

Answer 1

we know there are 180° in π radians, so how many degrees in 300° then?


`\bf \begin{array}{ccll} degr ees&radians\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 180&\pi \\ 300&r \end{array}\implies \cfrac{180}{300}=\cfrac{\pi }{r}\implies r=\cfrac{300\pi }{180}\implies \cfrac{5\pi }{3}`

Answer 2

`(5)/(3)\pi\ radians`

Explanation:

we know that

If the measures of the major arc CBD is equal to
`300` degrees

then

the measure of its corresponding central angle is equal to
`300` degrees

so

Convert degrees to radians

Remember that

`180\°=\pi \ radians`

so by proportion

Convert
`300\°` to radians

`(\pi)/(180)(radians)/(degrees) =(x)/(300)(radians)/(degrees)\\ \\x=300\pi /180\\ \\x=(5)/(3)\pi\ radians`