We have:
triangles have $3\times 60°=180°$
squares have $4\times 90°=360°$
pentagon have $5\times 108°= 540°$
hexagons have $6\times 120°=720°$
heptagons have $7\times 128.57° = 899.99 = 900°$
octagons have $8\times 135°=1080°$
What is the sum of the internal angles $\Pi$ in any $N$-sided polygons?
What is the value of one of the angle $\alpha$ in any $N$-sided polygons?
What is the value of $\Pi/\alpha$ in any $N$-sided polygons?
what is the value of $(\Pi-\alpha)/\alpha$ in any $N$-sided polygons?
i can draw the geometry.
$$\mbox{sum of internal angles of polygon with $N$ sides } = (N-2) * \pi $$
from which you can deduce the rest
$$\mbox{each internal angle $\alpha$} = \frac{(N-2) * \pi}{N} $$
$$ \pi/\alpha = \frac{N}{N-2} $$
$$ \frac{\pi - \alpha}{\alpha} = \frac{2}{N-2} $$
$$ \frac{sum\ of\ internal\ angles}{each\ angle\ \alpha} = N $$ $$ \frac{sum\ of\ internal\ angles - each\ angle\ \alpha}{each\ angle\ \alpha} = N -1 $$ where '$N$' is the number of sides of polygon and
$\pi = 180^{\circ}$
Note: in your question you have used $\Pi$ to denote something. both cases if it denotes $180 ^{\circ} $ or if it denotes sum of internal angles , have been solved in my answer . I don't want to use $\Pi$ again (as i have already used it to denote $180 ^{\circ} $ ) and confuse readers . Hope this helps .