How do you calculate angles of a polygon?

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How do you calculate angles of a polygon?

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Answer 1 · 2016-01-29T01:35:29

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
$alpha = (N-2)/N*180^o$

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How do you calculate angles of a polygon?

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