Find the magnitude, in radians and degrees, of the interior angle of a regular octagon.
Solution:
A regular octagon has \(8\) sides.
Interior angle of a regular polygon:
\[ \frac{(n-2)\times180^\circ}{n} \]
Substituting \(n=8\):
\[ \frac{(8-2)\times180^\circ}{8} \]
\[ \frac{6\times180^\circ}{8} \]
\[ 135^\circ \]
Now convert into radians:
\[ 135^\circ \times \frac{\pi}{180^\circ} \]
\[ \frac{3\pi}{4} \]
Therefore, the interior angle of a regular octagon is:
\[ 135^\circ \text{ or } \frac{3\pi}{4} \text{ radians} \]