Regular Polygons and their Interior Angles

Internal angle of a regular polygon with $n$ sides is $x=180^\circ-\frac{360^\circ}{n}$

Therefore $n=\frac{360^\circ}{180^\circ-x}$

Substituting this into expression for the internal angle of a polygon with $2n$ sides: $180^\circ-\frac{360^\circ}{2n}=\boxed{90^\circ+\frac{x}{2}}$

Internal angle of an $n$ -sided regular polygon is given by

$\begin{aligned} \theta(n) & = \frac {180(n-2)}n = \color{#3D99F6} 180 - \frac {360}n = x \\ \theta (2n) & = 180 - \frac {360}{2n} \\ & = 90 + \frac 12 \left({\color{#3D99F6} 180 - \frac {360}n} \right) & \small \color{#3D99F6} \text{Note that } 180 - \frac {360}n = x \\ & = \boxed{90 + \color{#3D99F6} x} \end{aligned}$