Question

What is the measure of one interior angle of a decagon with an apothem of 15 mm

Answer 1

now, we're assuming this is a regular decagon, namely a polygon with 10 sides, and regardless of perimeter or length of each side or apothem or even radius, the interior angles will be the same for all of them, large or small or tiny.

`\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ n=10 \end{cases}\implies 10\theta =180(10-2) \\\\\\ 10\theta =180(8)\implies 10\theta = 1440\implies \theta =\cfrac{1440}{10}\implies \theta =144`