Question

How do you calculate angles of a polygon?

Answer 1

Given only the lengths of polygon's sides, calculation of angles is possible for triangles and regular `N`-sided polygons.
In other cases angles cannot be defined.

Explanation:

In case of triangle, given all three sides `a`, `b` and `c`, we can use Theorem of Sines to get to the angles `alpha`, `beta` and `gamma = pi - alpha - beta`:
`a/sin(alpha) = b/sin(beta) = c/sin(gamma)`

For two unknown angles `alpha` and `beta` we have two equations:
`a/sin(alpha) = b/sin(beta)`
`a/sin(alpha) = c/sin(pi-alpha-beta)`
Solving them will give angles.

For `N`-sided polygons the interior angles are easily determined by a formula
`alpha = (N-2)/N*180^o`