Final Answer:
The correct values for x and y are 102 degrees and 9 degrees, respectively, so the correct (Option A) 102, 9.
Step-by-step explanation:
In the given figure, when two parallel lines (p and q) are intersected by two non-parallel lines (m and n), corresponding angles formed are congruent. The angle x is an alternate interior angle to the angle of 102 degrees, and the angle y is a corresponding angle to the angle of 9 degrees. By the properties of parallel lines and transversals, we can conclude that x is 102 degrees, and y is 9 degrees.
The angle x is formed by the intersection of line m with line q, and it is an alternate interior angle to the angle of 102 degrees formed by the intersection of line n with line q. Therefore, x = 102 degrees. Similarly, angle y is formed by the intersection of line n with line p, and it is a corresponding angle to the angle of 9 degrees formed by the intersection of line m with line p. Hence, y = 9 degrees.
In summary, the values of x and y are determined by the properties of angles formed by parallel and non-parallel lines intersected by a transversal. The correct values are x = 102 degrees and y = 9 degrees, leading to the correct answer of (Option A) 102, 9.