Question

which angle forms a linear pair with ∠mps?
angle rpn
angle rpm
angle mpj
angle mpk

Explanation:

Step1: Recall linear pair definition

A linear pair of angles are adjacent angles that form a straight line (sum to \(180^\circ\)), sharing a common side and vertex.

Step2: Analyze \(\angle MPS\) and options

• \(\angle RPN\): Not adjacent to \(\angle MPS\) to form a line.
• \(\angle RPM\): Adjacent to \(\angle MPS\)? Wait, re - evaluate. Wait, looking at the diagram (implied by the angle labels), \(\angle MPJ\): Wait, no. Wait, \(\angle MPS\) and \(\angle MPJ\)? Wait, no, let's think again. Wait, the correct adjacent angle forming a linear pair with \(\angle MPS\) should share a common side (ray \(PM\)) and the other sides form a straight line. Wait, among the options, \(\angle MPJ\) – no, wait, maybe I misread. Wait, the correct answer is Angle MPJ? No, wait, let's check again. Wait, a linear pair: two angles are adjacent and their non - common sides are opposite rays. So for \(\angle MPS\), the common vertex is \(P\), common side is \(PM\). The other side of \(\angle MPS\) is \(PS\), so the angle that forms a linear pair should have a side \(PJ\) (if \(PS\) and \(PJ\) are opposite rays). So \(\angle MPJ\) forms a linear pair with \(\angle MPS\) as they share \(PM\), and \(PS\) and \(PJ\) are opposite rays (forming a straight line), so their sum is \(180^\circ\).

Answer:

Angle MPJ