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Which of the following degree measures is equal to 
10 pi radians?
(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) 
3,600^(@)
(B) 
1,800^(@)
(c) 
180^(@)
(D) 
72^(@)

Which of the following degree measures is equal to 10π 10 \pi radians?\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) 3,600 3,600^{\circ} \newline(B) 1,800 1,800^{\circ} \newline(C) 180 180^{\circ} \newline(D) 72 72^{\circ}

Full solution

Q. Which of the following degree measures is equal to 10π 10 \pi radians?\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) 3,600 3,600^{\circ} \newline(B) 1,800 1,800^{\circ} \newline(C) 180 180^{\circ} \newline(D) 72 72^{\circ}
  1. Conversion factor: To convert radians to degrees, we use the conversion factor that 2π2\pi radians is equal to 360360 degrees. Therefore, to find the degree measure equivalent to 10π10\pi radians, we set up a proportion.
  2. Proportion setup: Using the proportion, we have: \newline(10π radians)×(360 degrees2π radians)=(102)×360 degrees(10 \pi \text{ radians}) \times (\frac{360 \text{ degrees}}{2\pi \text{ radians}}) = (\frac{10}{2}) \times 360 \text{ degrees}
  3. Expression simplification: Simplifying the expression, we get: 5×3605 \times 360 degrees =1800= 1800 degrees
  4. Final result: Therefore, 10π10\pi radians is equal to 18001800 degrees.

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