Final answer:
Lines l and m are parallel, and the measurement of angle 6 and angle 7 are given by two equations set equal because they are alternate interior angles. Solving for x, we find that x = 15, leading to the conclusion that the measurement of angle 6 is 45 degrees.
Step-by-step explanation:
If lines l and m are parallel and angle 6 is represented by 4x - 15 and angle 7 by x + 30, they are alternate interior angles and hence equal. Therefore, we have the equation 4x - 15 = x + 30. Solving for x, we subtract x from both sides to get 3x - 15 = 30, and then add 15 to both sides to get 3x = 45. Dividing by 3, we find that x = 15. Substituting x back into either equation, m∠6 or m∠7, we get that m∠6 = 4(15) - 15, which simplifies to 60 - 15, and therefore m∠6 = 45 degrees.