Question

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.

Explanation:

• Vertical angles: Vertical angles are formed when two lines intersect. They are opposite each other and are equal in measure.
• Linear pair: A linear pair of angles is formed when two adjacent angles form a straight line (sum to \(180^{\circ}\)).

If ray \(LR\) is opposite ray \(LM\), then \(\angle RLN\) and \(\angle MLK\) are formed by the intersection of two lines (\(LK - LN\) and \(LM - LR\)). They are opposite each other.

• For \(\angle RLN\) and \(\angle MLN\): They do not satisfy the vertical - angle condition (not formed by two intersecting lines in the required way).
• For \(\angle RLN\) and \(\angle KLM\): They are not adjacent to form a linear pair.
• For \(\angle RLN\) and \(\angle KLN\): \(\angle KLN\) is a straight angle (\(180^{\circ}\)), and \(\angle RLN\) is not adjacent to \(\angle KLN\) in the linear - pair sense.

Answer:

Angles \(RLN\) and \(MLK\) would be vertical angles.