Final answer:
To find missing angles, methods like trigonometric functions and the Pythagorean theorem are used, depending on the problem. A protractor or calculations involving radians may be applied, and solutions should always be checked for reasonableness.
Step-by-step explanation:
To find the measure of the missing angles in a given problem, we can use various methods depending on the context. For vector addition problems, such as when finding the resultant of two vectors, one would use trigonometrical relationships to determine the direction of the resultant based on the angle it makes with the reference frame. If we have a parallelogram formed by vectors, as seen in the example provided, the diagonal of the parallelogram gives the resultant, and using a protractor can help in measuring the angles directly.
In other cases involving right-angled triangles, such as determining the distance on a screen from interference patterns or calculating tensions in a system of forces, the Pythagorean theorem is often applied, and trigonometric functions such as sine, cosine, and tangent are used to find the missing angle measures. After obtaining the solutions, it is important to verify if they are reasonable. For example, checking whether the angles don't exceed 90° in an interference pattern or that the computed results make sense in the context of the problem.
When substituting values into equations, it is important to use consistent units, and if angles are involved, they are frequently expressed in radians. It is crucial to also double-check the coherence of the results to ensure that they logically fit within the problem's parameters.