Which pair of angles forms a linear pair in standard position?

• A. $\angle \mathrm{mrn}$ and $\angle \mathrm{nro}$
• B. $\angle \mathrm{prl}$ and $\angle \mathrm{lrm}$
• C. $\angle \mathrm{lrp}$ and $\angle \mathrm{orp}$
• D. $\angle \mathrm{orp}$ and $\angle \mathrm{mrn}$

Answer: (D)

Verified step by step guidance

1. Step 1: Understand what a linear pair of angles is. A linear pair consists of two adjacent angles whose non-common sides form a straight line, meaning their measures add up to 180 degrees.
2. Step 2: Identify the angles given in the problem and their positions. Since the problem mentions angles by their vertex and points (e.g., mrn, nro, prl, lrm, lrp, orp), recognize that each angle is named by three points, with the middle letter representing the vertex.
3. Step 3: Visualize or sketch the angles in standard position, placing the vertex at the origin and the rays extending from it. This helps to see which angles share a common side and whether their other sides form a straight line.
4. Step 4: Check each pair of angles to see if they are adjacent (share a vertex and a side) and if their non-common sides form a straight line (180 degrees). This confirms if they form a linear pair.
5. Step 5: Conclude that the pair 'orp and mrn' forms a linear pair because they are adjacent angles with their non-common sides lying on a straight line, satisfying the definition of a linear pair.