Find the magnitude, in radians and degrees, of the interior angle of a regular heptagon.
Solution:
A regular heptagon has \(7\) sides.
Interior angle of a regular polygon:
\[ \frac{(n-2)\times180^\circ}{n} \]
Substituting \(n=7\):
\[ \frac{(7-2)\times180^\circ}{7} \]
\[ \frac{900^\circ}{7} \]
\[ 128\frac{4}{7}^\circ \]
Now convert into radians:
\[ \frac{900^\circ}{7}\times\frac{\pi}{180^\circ} \]
\[ \frac{5\pi}{7} \]
Therefore, the interior angle of a regular heptagon is:
\[ 128\frac{4}{7}^\circ \text{ or } \frac{5\pi}{7} \text{ radians} \]