An arc on a circle measures $250°$. Within which range is the radian measure of the central angle?

• A. $4<x<5$
• B. $2<x<3$
• C. $1<x<2$
• D. $3<x<4$

Answer: (D)

Verified step by step guidance

1. Recall the relationship between degrees and radians: to convert degrees to radians, use the formula \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).
2. Apply this formula to the given central angle of 250 degrees: calculate \(x = 250 \times \frac{\pi}{180}\).
3. Simplify the fraction \(\frac{250}{180}\) by dividing numerator and denominator by their greatest common divisor, which is 10, to get \(\frac{25}{18}\).
4. Express the radian measure as \(x = \frac{25}{18} \pi\).
5. Estimate the value of \(x\) by approximating \(\pi \approx 3.14\) and check which interval among the given options \$3 < x < 4\(, \)4 < x < 5\(, \)2 < x < 3\(, or \)1 < x < 2$ the radian measure falls into.