Let us first understand these two types of angles that are mentioned in the question.
Linear pair of angles:
These are adjacent angles and when they are combined they form a 180° angle.
Vertical angles:
These are the opposite angles that are formed when two lines intersect.
Now let us analyze each of the given options.
a. 1 and 3 are a linear pair (wrong) since they are not adjacent angles.
b. 1 and 3 are vertical angles (correct) since they are opposite angles.
c. 8 and 9 are a linear pair (wrong) since they are adjacent but they do not form a 180° angle.
d. 8 and 9 are vertical angles (wrong) since they are not opposite angles.
e. 3 and 4 are a linear pair (correct) since they are adjacent and also form a 180° angle.
f. 3 and 4 are vertical angles (wrong) since they are not opposite angles.
Therefore, only option b and e are correct.
b. 1 and 3 are vertical angles (correct) since they are opposite angles.
e. 3 and 4 are a linear pair (correct) since they are adjacent and also form a 180° angle.