Final answer:
To measure angles ∠a and ∠b, a protractor is used and their sum is found by simply adding the measurements. The relationship between the angles depends on the context, which could imply a right triangle if using the Pythagorean theorem. In vector diagrams, the theorem helps in finding the length of the resultant vector.
Step-by-step explanation:
To measure ∠a and ∠b and find their sum, we would typically use a protractor to measure each angle. You would then add the angular measurements together to get their sum. How ∠a and ∠b are related could depend on the context - whether they are adjacent angles, supplementary angles, complementary angles, etc. However, based on the various uses of the Pythagorean theorem (a² + b² = c²) in the provided information, if ∠a and ∠b are the angles at the base of a right triangle, their sum would be less than 90 degrees since the third angle is the right angle (90 degrees).
If given vector diagrams, as suggested in the information, we could use the lengths of vectors and their angles to determine the magnitude and direction of resultant vectors. For example, in a right triangle, the Pythagorean theorem helps us find the length of the hypotenuse c, which represents the resultant vector when legs a and b represent the component vectors.