Question

which angles are supplementary angles? ∠onp and ∠lkn ∠onp and ∠jkl ∠onp and ∠omk ∠onp and ∠mlk

Explanation:

Step1: Recall supplementary - angles definition

Two angles are supplementary if their sum is 180 degrees. When two lines intersect, adjacent angles formed are supplementary.

Step2: Analyze the given angle - pairs

In the figure, when two lines intersect, adjacent angles share a common side and a common vertex. For example, if we consider the intersection of lines, adjacent angles around a point on a line sum to 180 degrees. Looking at the pairs:

• ∠ONP and ∠LNK are vertical angles (opposite angles formed by the intersection of two lines), not supplementary.
• ∠ONP and ∠JNK are not adjacent angles in a way that they sum to 180 degrees.
• ∠ONP and ∠ONK are adjacent angles. They share a common side (ray $\overrightarrow{ON}$) and a common vertex (point N) and together form a straight - line. So, ∠ONP+∠ONK = 180 degrees.
• ∠ONP and ∠MNK are not adjacent angles that sum to 180 degrees.

Answer:

∠ONP and ∠ONK