Final answer:
Stu's approach to calculating only four angles with certainty is more plausible because it suggests that the calculations are based on verifiable information, adhering to the constraints and principles of geometry. Gail's method might contain errors if it doesn't align with logical limits, such as surpassing maximum possible measures in interference patterns.
Step-by-step explanation:
Understanding Angle Measurement
When determining the measurements of angles in a geometric problem, it is crucial to consider the given information and known principles. For instance, the sum of angles in a triangle is always 180 degrees, and if calculating angles formed by interference patterns, they should not exceed 90 degrees. When taking such facts into account, it's possible that Gail's answer includes some incorrect measures if she claims to calculate more than what the information logically permits, such as angles in an interference pattern being larger than 90 degrees. Therefore, Stu's assertion of calculating only four angles with certainty seems more plausible and suggests that Stu is only considering the information that can be verified with certainty.
In mathematics, it is also important to check the reasonableness of an answer. One should ask if the magnitude, orientation, and measurements make logical sense according to the principles at hand. Misapplied theorems like the Pythagorean theorem can lead to incorrect results. Hence, when we talk about the certainty within mathematics or physics, it often involves consistently applying the correct postulates and principles, while being mindful that all parts of our calculation or theory must align. Following these steps will help in getting a reliable and verifiable result.