# Range of Interior Angles of Polygons

$\newcommand{\degree}{{^\circ}}$

Considering the method of of interior angles in surveying a traverse, what is the maximum range of any one interior angle? Also, what is the practical range of any one interior angle?

In other words, what is the maximum angle of an interior angle of a polygon?

My first thought is that the maximum angle would be $180\degree$, but that makes no sense. So, I would suggest the maximum angle would be $360\degree$. However, the maximum practical range would be $359\degree$. Or even more specifically $359 \degree 59'59''$.

Is this correct?

First of all ,angles can be measured continuously in radians ( in the interval $[0,2\pi]$), not only in discrete divisions as: degrees, minutes, seconds. If you look for an upper bound there are two cases:
• if the polygon is convex, the upper bound is $\pi$ (180 degrees). Note that this is an upper bound: it cannot be attained, but you can get as close as you want to it.
• if the polygon is concave (for example a concave quadrilateral) then the upper bound is $2\pi$ (360 degrees). Again, the same remark applies: it cannot be attained, but you can get as close as you want.