Question

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

Answer 1

Answer:

$\frac{5}{3}\pi\ radians$

Step-by-step 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

$\frac{\pi}{180}\frac{radians}{degrees} =\frac{x}{300}\frac{radians}{degrees}\\ \\x=300\pi /180\\ \\x=\frac{5}{3}\pi\ radians$

Answer 2

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

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