Final Answer:
The measure of angle b in the diagram is:
C. 52 degrees; Vertical angles
Step-by-step explanation:
In the given diagram, angle b measures 52 degrees, and this conclusion is justified by the vertical angles theorem. According to the vertical angles theorem, when two lines intersect, they form pairs of vertical angles that are congruent. In this case, angle b and the adjacent angle (opposite angle to b) are vertical angles because they are formed by the intersection of two lines.
Therefore, the measure of angle b is equal to the measure of its vertical angle counterpart. As a result, the correct choice is C, with 52 degrees representing the measure of angle b and the vertical angles relationship supporting this conclusion.
Vertical angles are a pair of non-adjacent angles formed by the intersection of two lines. These angles are always congruent, meaning they have the same measure. In the context of the given diagram, the vertical angles theorem is applied to establish the measure of angle b. This theorem is a fundamental concept in geometry and helps in determining angle measures when lines intersect.
In this specific scenario, recognizing the vertical angles and their equality is crucial in arriving at the correct measure for angle b. Overall, the application of the vertical angles theorem simplifies the analysis of angles formed by intersecting lines and contributes to the solution of geometric problems.