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Parallel lines p and q are cut by two non-parallel lines, m and n, as shown in the figure. The value of x is __ degrees, and the value of y is __ degrees.

A) 102, 9

B) 1150, 9

C) 9, 102

D) 9, 1150

User Dickbarba
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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.

User HKTonyLee
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