To determine the measure of a central angle in radians and identify which range it falls into, follow these steps:
### Step-by-Step Solution:
1. Convert Degrees to Radians:
- First, we need to convert the angle from degrees to radians. The formula to convert degrees to radians is:
[tex]\[
\text{angle in radians} = \text{angle in degrees} \times \left(\frac{\pi}{180}\right)
\][/tex]
- For an angle of [tex]\(295^{\circ}\)[/tex]:
[tex]\[
\text{angle in radians} = 295 \times \left(\frac{\pi}{180}\right)
\][/tex]
2. Calculate the Angle in Radians:
- Perform the calculation:
[tex]\[
\text{angle in radians} = 295 \times \left(\frac{\pi}{180}\right) \approx 5.1487212933832724
\][/tex]
3. Determine the Range:
- Now, compare the calculated angle in radians with the given ranges:
[tex]\[
\begin{aligned}
0 & \quad \text{to} \quad \frac{\pi}{2} \quad (\approx 0 \text{ to } 1.5708) \\
\frac{\pi}{2} & \quad \text{to} \quad \pi \quad (\approx 1.5708 \text{ to } 3.1416) \\
\pi & \quad \text{to} \quad \frac{3\pi}{2} \quad (\approx 3.1416 \text{ to } 4.7124) \\
\frac{3\pi}{2} & \quad \text{to} \quad 2\pi \quad (\approx 4.7124 \text{ to } 6.2832) \\
\end{aligned}
\][/tex]
- Comparing [tex]\(5.1487212933832724\)[/tex] with these ranges:
[tex]\[
4.7124 \quad \text{to} \quad 6.2832
\][/tex]
4. Conclusion:
- The angle [tex]\(5.1487212933832724\)[/tex] radians falls within the range:
[tex]\[
\frac{3\pi}{2} \quad \text{to} \quad 2\pi \quad (\approx 270^{\circ} \text{ to } 360^{\circ})
\][/tex]
### Final Answer:
The measure of the central angle in radians, [tex]\(5.1487212933832724\)[/tex], is within the range:
[tex]\[
\frac{3\pi}{2} \quad \text{to} \quad 2\pi \quad \text{radians}
\][/tex]
