We have a transversal with two parallel lines:
If ∠1 =60°
∠1 = ∠8 using the alternate exterior angles property.
Also
∠1 =∠4 and ∠8 = ∠5 using the corresponding angles ( they are vertical angles)
Now, ∠1 and ∠2 are supplementary angles, they together form a right line.
Supplementary angles are equal to 180°, then, we can deduce the next equation:
∠1 + ∠2 = 180°
Replacing ∠1 = 60°
60° + ∠2 = 180°
Solve for ∠2:
∠2 = 180° - 60°
∠2 = 120°
Then ∠2 = ∠7 using the alternate exterior angles property.
Also
∠7 = ∠6 and ∠2 = ∠3
So far we got:
∠1 = ∠4 = ∠5 = ∠8 = 60°
and
∠2 = ∠3 = ∠6 = ∠7 = 120°
Therefore, the correct answer is the third option.