Maximum number of right interior angles in an $n$-gon

Question

What is the maximum number of right interior angles in an $n$-gon for $n\ge 3$?

A naive approach based on summing the interior angles gives an upper bound of $\lceil 2(n+2)/3\rceil-1$; however I doubt that bound is attainable for $n\ge 10$. From my trial-and-error, I'd expect the result to grow like $n/2$.

Answer 1

Your upper bound is attainable. Consider the polygon with two consecutive right angles, followed by an angle close to $2\pi$, then two more consecutive right angles, and so on.

Here's an example for $n = 7$ with $5$ right angles.