Answer:
The central angle is within the range π to 3π/2
Step-by-step explanation:
To convert from degrees to radians, we multiply the angle in degrees by 180/π.
To convert from radians to degree, we multiply the angle in radians by 180°/π.
π/2 = π/2 X 180°/π= 90°
π rad = π X 180°/π= 180°
3π/2 = 3π/2 X 180°/π= 270°
2π = 2π X 180°/π= 360°
Therefore the angle 250 which is between 180 and 270 is within the range :
π to 3π/2
The central angle is within the range π to 3π/2
The measure of the arc is given as:
[tex]A = 250^o[/tex]
Start by converting the measure of the arc from degrees to radian using:
[tex]\theta = A \times \frac{\pi}{180}[/tex]
Substitute 250 for A in the above equation
[tex]\theta = 250 \times \frac{\pi}{180}[/tex]
Multiply 250 and pi
[tex]\theta = \frac{250\pi}{180}[/tex]
Divide 250 by 180
[tex]\theta = 1.34\pi[/tex]
[tex]1.34\pi[/tex] is between [tex]\pi[/tex] and [tex]\frac{3\pi}{2}[/tex]
Hence, the central angle is within the range π to 3π/2
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