Final Answer:
The correct value of x that makes m || n is option c) x = 22.
Step-by-step explanation:
To determine the value of x that makes lines m and n parallel, we need to consider the properties of parallel lines. Two lines are parallel if and only if the corresponding angles are congruent. In this case, the angles formed by the transversal x with lines m and n must be equal.
Let's denote the angles formed as ∠1 and ∠2. If x = 22, then ∠1 = 22°. To show that lines m and n are parallel, we also need to consider the alternate interior angles. If ∠1 = 22°, then the alternate interior angle ∠3 formed by x and line n is also 22°. This ensures that corresponding angles and alternate interior angles are congruent, establishing the parallelism of lines m and n.
In a mathematical context, the property that justifies this is the Converse Alternate Interior Angles Theorem. According to this theorem, if two lines are cut by a transversal, and the alternate interior angles are congruent, then the lines are parallel. Therefore, x = 22 satisfies the conditions for parallel lines, making it the correct answer.
In conclusion, option c) x = 22 is the final answer because it satisfies the angle conditions required for lines m and n to be parallel.