This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Answer
Step 1: Find the value of . The angle and the angle form a linear pair on a straight line. Angles on a straight line sum to .
Step 2: Find the value of . The sum of the interior angles in a triangle is . The three interior angles are , , and . Substitute the value of found in Step 1:
The values are: x = \text{88^\circ} y = \text{51^\circ}
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Find the value of x. The angle x and the 92^ angle form a linear pair on a straight line.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.