Using the concept of transversal line passing through parallel lines, we can say that ∠3 is congruent to ∠8 since the two angles are corresponding angles.
Note that since ∠1 and ∠9 are on the same line, we cannot say that the two angles are congruent. On the otherhand, ∠3 and ∠10 are also on the same line and ∠3 and ∠4 are also on line a. This means that the angles cannot be alternate interior angles.
Thus, the correct answer for question #1 is option D.
For question #2, since ∠8 and ∠13 are interior angles on the same side of the transversal, the two angles must be supplementary.
On the other hand, ∠7 and ∠13 are alternate interior angles. Thus, the angles must be congruent.
Similarly, ∠1 and ∠9 are corresponding angles. Thus, the angles are also congruent.
However, ∠9 and ∠7 are not on the same transversal line. Therefore, we cannot obtain a conjecture on these angles. Thus, the correct answer must be option B.
For question #3, if ∠4 and ∠9 are congruent, then line c and line d must be parallel. Thus, ∠4 and ∠9 must be alternate interior angles. This means the correct answer is option D.
For question 4, if ∠1 and ∠13 are congruent, then ∠1 are ∠13 must be alternate exterior angles. Thus, line c and line d must be parallel. This means the correct answer must be option A.