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:

Step1: Recall the definition of vertical angles

Vertical angles are formed when two lines intersect. They are opposite each other and are equal in measure.

Step2: Analyze each option

• Option 1: Angles \(RLN\) and \(MLK\) would be vertical angles

When ray \(LR\) is opposite ray \(LM\), \(\angle RLN\) and \(\angle MLK\) are formed by the intersection of two lines (the line containing \(KLN\) and the line containing \(MLR\)). They are opposite each other.

• Option 2: Angles \(RLN\) and \(MLN\) would be vertical angles

\(\angle RLN\) and \(\angle MLN\) do not satisfy the condition of vertical angles (not formed by the intersection of two lines in the required way).

• Option 3: Angles \(RLN\) and \(KLM\) would be a linear pair

A linear pair of angles is adjacent and their non - common sides form a straight line. \(\angle RLN\) and \(\angle KLM\) are not adjacent.

• Option 4: Angles \(RLN\) and \(KLN\) would be a linear pair

\(\angle RLN\) and \(\angle KLN\) are not adjacent in the way required for a linear pair (a linear pair has two adjacent angles whose non - common sides form a straight line).

Answer:

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