Express a central angle measuring 3.2 radians in terms of degrees.

The correct option is 183.27°.

To convert an angle from radians to degrees, we use the conversion factor derived from the relationship between radians and degrees. A full revolution around a circle is equal to 2π radians or 360 degrees. Therefore:

$\pi \text{radians}=180°$

Dividing both sides by π gives the measure of 1 radian in degrees:

$1\text{radian}=\frac{180°}{\pi }$

To convert any angle given in radians to degrees, we multiply the angle measure by $\frac{180°}{\pi }$:

$\text{Angle in degrees}=\text{Angle in radians}\times \frac{180°}{\pi }$

Given that the central angle is 3.2 radians, we substitute this value into our conversion equation:

$\text{Angle in degrees}=3.2\times \frac{180°}{\pi }$

Using the fractional approximation of π as $\frac{22}{7}$:

$\text{Angle in degrees}=3.2\times \frac{180°\times 7}{22}$

$\text{Angle in degrees}=\frac{4032}{22}°\approx 183.27°$

Hence, a central angle measuring 3.2 radians is equal to approximately 183.27°.