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Which of the following radian measures is equal to 
180^(@) ?
(The number of degrees of arc in a circle is 360 . The number of radians of arc in a circle is 
2pi.)
Choose 1 answer:
(A) 
(pi)/(2) radians
(B) 
(pi)/(3) radians
(C) 
(pi)/(4) radians
(D) 
pi radians

Which of the following radian measures is equal to 180 180^{\circ} ?\newline(The number of degrees of arc in a circle is 360360 . The number of radians of arc in a circle is 2π 2 \pi .)\newlineChoose 11 answer:\newline(A) π2 \frac{\pi}{2} radians\newline(B) π3 \frac{\pi}{3} radians\newlineC) π4 \frac{\pi}{4} radians\newline(D) π \pi radians

Full solution

Q. Which of the following radian measures is equal to 180 180^{\circ} ?\newline(The number of degrees of arc in a circle is 360360 . The number of radians of arc in a circle is 2π 2 \pi .)\newlineChoose 11 answer:\newline(A) π2 \frac{\pi}{2} radians\newline(B) π3 \frac{\pi}{3} radians\newlineC) π4 \frac{\pi}{4} radians\newline(D) π \pi radians
  1. Understanding degrees and radians: Understand the relationship between degrees and radians. We know that 360360 degrees is equal to 2π2\pi radians. Therefore, to convert degrees to radians, we use the formula radians=degrees×(π180)\text{radians} = \text{degrees} \times \left(\frac{\pi}{180}\right).
  2. Converting 180180 degrees to radians: Convert 180180 degrees into radians using the formula from Step 11. By substituting 180180 degrees into the formula, we get 180180 degrees =180×(π180)=π= 180 \times \left(\frac{\pi}{180}\right) = \pi radians.
  3. Choosing the correct option for 180180 degrees: Choose the correct option of radians for 180180 degrees. The correct option is π\pi radians, which is equivalent to 180180 degrees.

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