The supplementary angles 9x - 2 and 10y + 6 result from a straight line. Corresponding angles 9x - 2 and 5x + 54 are set equal, leading to x = 14 and reinforcing geometric relationships in the parallel line configuration.
The angles 9x - 2 and 10y + 6 are supplementary because they form a straight line. Moreover, 9x - 2 and 5x + 54 are corresponding angles as l and m are parallel lines intersected by a transversal. Utilizing the fact that corresponding angles are congruent, we set these two expressions equal to each other:
9x - 2 = 5x + 54
Simplifying the equation, we combine like terms:
4x = 56
By isolating x, we find x = 14. This solution establishes the angle measures in terms of x, providing a comprehensive understanding of the geometric relationships within the given parallel lines and transversal scenario. The consistent application of angle properties and parallel line theorems facilitates the derivation of x and further validates the supplementary nature of the identified angles.