Option A: ∠5 and ∠13 are alternate interior angles with angle 3.
Solution:
To find which angles are alternate interior angles with angle 3:
Option A: ∠5 and ∠13
If t and u are parallels, then r is a transversal.
3 and 13 are alternate interior angles.
If r and s are parallels, then t is a transversal.
3 and 5 are alternate interior angles.
Therefore ∠5 and ∠13 are alternate interior angles with angle 3.
Hence it is true.
Option B: ∠7 and ∠15
∠7 is a corresponding angle of ∠3 on the same side of the transversal.
∠15 is a corresponding angle of ∠3 on the same side of the transversal.
So, ∠7 and ∠15 are not alternate interior angles with angle 3.
Hence it is not true.
Option C: ∠6 and ∠16
∠6 is an alternate exterior angle of ∠3.
∠16 is an alternate exterior angle of ∠3.
So, ∠6 and ∠16 are not alternate interior angles with angle 3.
Hence it is not true.
Option D: ∠8 and ∠14
∠8 is an interior angle on the same side.
∠14 is an interior angle on the same side.
So, ∠8 and ∠14 are not alternate interior angles with angle 3.
Hence it is not true.
Therefore ∠5 and ∠13 are alternate interior angles with angle 3.
Option A is the correct answer.
