Angle klm and angle mln are a linear pair. ray lr is to be added to the diagram so that it is opposite ray lm. which is true about angle rln that would be formed? angles rln and mlk would be vertical angles. angles rln and mln would be vertical angles. angles rln and klm would be a linear pair. angles rln and kln would be a linear pair.

Angles RLN and MLK would be vertical angles.
Right. Vertical angles are formed when their sides share the same lines. RL shares the same line with LM and NL shares the same line with LK (see the attached diagram), so that means both angles form a vertical pair.

Angles RLN and MLN would be vertical angles.
Wrong. They are linear pairs, because they are adjacent and supplementary. Adjacent angles share a side – in this case, LN. Supplementary angles sum 180°, which you can see is right because the other sides (ML and RL) are in the same line. RLN and MLN sum the same as the size of RLM, which is a line, so it’s 180°. 

Angles RLN and KLM would be a linear pair.
Wrong. They would be a vertical pair (see definition of vertical pair in the first option). RL is opposed to LM and LN is opposed to KL.

Angles RLN and KLN would be a linear pair.
Wrong. KLN is actually a line, so it’s actually 180°, so it can’t be a linear pair with KLN. Linear pairs sum 180°, which is impossible because KLN itself is already 180°, so any sum will throw a higher number.