Question

i and no are parallel lines. which angles are supplementary angles? ∠onp and ∠jki ∠onp and ∠mnk ∠onp and ∠lkn ∠onp and ∠onk

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\).

Step2: Analyze \(\angle ONP\) and \(\angle ONK\)

Since \(\overrightarrow{NO}\) is a straight line, \(\angle ONP+\angle ONK = 180^{\circ}\) (linear - pair of angles). A linear - pair of angles is formed when two adjacent angles form a straight line.

For \(\angle ONP\) and \(\angle JKI\): There is no property (like parallel - line properties or linear - pair) that makes their sum \(180^{\circ}\).
For \(\angle ONP\) and \(\angle MNK\): \(\angle MNK\) and \(\angle ONP\) are vertical angles (if we consider the intersection at \(N\)), and vertical angles are equal, not supplementary.
For \(\angle ONP\) and \(\angle LKN\): Since \(\overrightarrow{NO}\parallel\overrightarrow{JL}\), \(\angle ONP=\angle LKN\) (corresponding angles), and they are equal, not supplementary.

Answer:

\(\angle ONP\) and \(\angle ONK\)