Which of the following degree measures is equal to 10π radians?(The number of degrees of arc in a circle is 360 . The number of radians of arc in a circle is 2π.)Choose 1 answer:(A) 3,600∘(B) 1,800∘(C) 180∘(D) 72∘
Q. Which of the following degree measures is equal to 10π radians?(The number of degrees of arc in a circle is 360 . The number of radians of arc in a circle is 2π.)Choose 1 answer:(A) 3,600∘(B) 1,800∘(C) 180∘(D) 72∘
Conversion factor: To convert radians to degrees, we use the conversion factor that 2π radians is equal to 360 degrees. Therefore, to find the degree measure equivalent to 10π radians, we set up a proportion.
Proportion setup: Using the proportion, we have: (10π radians)×(2π radians360 degrees)=(210)×360 degrees
Expression simplification: Simplifying the expression, we get: 5×360 degrees =1800 degrees
Final result: Therefore, 10π radians is equal to 1800 degrees.