Angles and triangle laws
Cosine law when the known angle sits between the two known sides; sine law when an angle faces a known side.
A worked example
For sides 7 and 10 with 55° between them, c^2 = 7^2 + 10^2 - 2(7)(10)cos 55° = 68.7, so c = 8.3.
The mistake people actually make
Interior angles of an n-sided polygon sum to (n - 2) x 180, not n x 180. Co-interior angles on the same side of a transversal add to 180°, they are not equal.