there is a circle, one angel is shaded 144 degrees what is the second angel in pi

1 answer

In a circle, the sum of angles around a point is \(360\) degrees. If one angle is shaded \(144\) degrees, we can find the remaining angle (the unshaded angle) by subtracting:

\[ 360^\circ - 144^\circ = 216^\circ \]

To convert \(216\) degrees into radians, we use the conversion factor \(\frac{\pi \text{ radians}}{180^\circ}\):

\[ 216^\circ \times \frac{\pi \text{ radians}}{180^\circ} = \frac{216\pi}{180} = \frac{12\pi}{10} = \frac{6\pi}{5} \]

Thus, the second angle in radians is:

\[ \frac{6\pi}{5} \]