Final answer:
By using the Converse Corresponding Angles Postulate to set the angles equal to each other (3x - 25 = 2x + 17), we solve for x and find that x = 42. This confirms that lines m and n are parallel.
Step-by-step explanation:
To find the value of x such that m || n, we can use the fact that if two lines are parallel, then their corresponding angles are equal. This is known as the Converse Corresponding Angles Postulate. Therefore, we set the two expressions equal to each other since they represent corresponding angles.
(3x - 25) = (2x + 17)
To solve for x, we must first collect like terms:
Here, we used the Converse Corresponding Angles Postulate to determine that the lines are parallel (m || n) when corresponding angles are equal.