Question

What is the measure of one angle in a regular 25-gon?

Answer 1

The sum of the interior angles in an n-gon is \[\sum angles = 180(n-2)\]Since we have a regular 25-gon, all of the angles will be equal in measure. So, each angle will be:\[m \angle X=\frac{180(n-2)}{n} = \frac{180\times 23}{25}=165.6 \deg\]