To solve for an angle in a triangle when all three side measurements are known, the Law of Cosines can be applied. This law allows for the calculation of any angle based on the lengths of the sides. The angles are denoted as A, B, and C, while the corresponding opposite sides are labeled a, b, and c. Understanding the validity of the Law of Cosines is encouraged, and resources for proof are available. Utilizing these methods will effectively yield the desired angle measurement.