Question

which angles are supplementary angles?

∠mnk and ∠lkn ∠mnk and ∠onk
∠mnk and ∠jki ∠mnk and ∠onp
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Explanation:

Step1: Recall the definition of supplementary angles

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

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

Since \(ON\) is a straight line (a straight - line has an angle measure of \(180^{\circ}\)), and \(\angle MNK+\angle ONK\) forms a linear pair (they are adjacent angles on a straight line). By the linear - pair postulate, if two angles form a linear pair, then they are supplementary.

Step3: Analyze other options

• For \(\angle MNK\) and \(\angle LKN\): There is no information to suggest their sum is \(180^{\circ}\).
• For \(\angle MNK\) and \(\angle JKI\): There is no information to suggest their sum is \(180^{\circ}\).
• For \(\angle MNK\) and \(\angle ONP\): \(\angle ONP\) and \(\angle ONK\) are vertical angles (\(\angle ONP=\angle ONK\)), and \(\angle MNK+\angle ONP=\angle MNK + \angle ONK

eq180^{\circ}\) (because \(\angle MNK+\angle ONK = 180^{\circ}\) and \(\angle ONP=\angle ONK\), so \(\angle MNK+\angle ONP\) is not a supplementary pair in the way of non - adjacent angles here).

Answer:

\(\angle MNK\) and \(\angle ONK\)