Find the magnitude, in radians and degrees, of the interior angle of a regular pentagon.
Solution:
A regular pentagon has \(5\) sides.
Interior angle of a regular polygon:
\[ \frac{(n-2)\times180^\circ}{n} \]
Substituting \(n=5\):
\[ \frac{(5-2)\times180^\circ}{5} \]
\[ \frac{3\times180^\circ}{5} \]
\[ 108^\circ \]
Now convert into radians:
\[ 108^\circ \times \frac{\pi}{180^\circ} \]
\[ \frac{3\pi}{5} \]
Therefore, the interior angle of a regular pentagon is:
\[ 108^\circ \text{ or } \frac{3\pi}{5} \text{ radians} \]