Find the magnitude, in radians and degrees, of the interior angle of a regular duodecagon.
Solution:
A regular duodecagon has \(12\) sides.
Interior angle of a regular polygon:
\[ \frac{(n-2)\times180^\circ}{n} \]
Substituting \(n=12\):
\[ \frac{(12-2)\times180^\circ}{12} \]
\[ \frac{10\times180^\circ}{12} \]
\[ 150^\circ \]
Now convert into radians:
\[ 150^\circ \times \frac{\pi}{180^\circ} \]
\[ \frac{5\pi}{6} \]
Therefore, the interior angle of a regular duodecagon is:
\[ 150^\circ \text{ or } \frac{5\pi}{6} \text{ radians} \]