Since lines l and m are parallel, we know that angles 1 and 5 are corresponding angles and are therefore congruent. Also, angles 4 and 8 are corresponding angles and are congruent.
We also know that angles 1 and 4 are vertical angles, so they are congruent, and angles 2 and 3 are vertical angles, so they are congruent.
Thus, we can set up the following equation:
m∠7 = m∠8 - m∠5 = m∠4 - m∠5
We are given that m∠2 = 120°, so we can use this to find m∠1:
m∠1 + m∠2 = 180° (since angles 1 and 2 are supplementary)
m∠1 + 120° = 180°
m∠1 = 60°
Since angles 1 and 5 are congruent, we know that m∠5 = 60°.
We are also given that angles 1 and 3 are complementary, so we can use this to find m∠3:
m∠1 + m∠3 = 90°
60° + m∠3 = 90°
m∠3 = 30°
Now we can find m∠4:
m∠1 + m∠4 = 180° (since angles 1 and 4 are supplementary)
60° + m∠4 = 180°
m∠4 = 120°
Finally, we can use these values to find m∠7:
m∠7 = m∠4 - m∠5
m∠7 = 120° - 60°
m∠7 = 60°
Therefore, m∠7 is 60°.