Question

select all the pairs of alternate exterior angles. ∠jki and ∠onk ∠onp and ∠jki ∠jkn and ∠jki ∠mnp and ∠lki

Explanation:

Step1: Recall alternate exterior angles definition

Alternate exterior angles are non - adjacent angles that lie outside two lines and on opposite sides of a transversal.

Step2: Analyze each pair

• For \(\angle JKI\) and \(\angle ONK\):
• Lines \(MO\) and \(JL\) are intersected by transversal \(PI\). \(\angle JKI\) and \(\angle ONK\) lie outside \(MO\) and \(JL\) and on opposite sides of \(PI\).
• For \(\angle ONP\) and \(\angle JKI\):
• Lines \(MO\) and \(JL\) are intersected by transversal \(PI\). \(\angle ONP\) and \(\angle JKI\) do not satisfy the alternate exterior angles condition as \(\angle ONP\) is adjacent to the intersection on \(MO\) in a way that is not alternate exterior.
• For \(\angle JKN\) and \(\angle JKI\):
• These are adjacent angles (they share a common side \(JK\)) and not alternate exterior angles.
• For \(\angle MNP\) and \(\angle LKI\):
• Lines \(MO\) and \(JL\) are intersected by transversal \(PI\). \(\angle MNP\) and \(\angle LKI\) lie outside \(MO\) and \(JL\) and on opposite sides of \(PI\).

Answer:

\(\angle JKI\) and \(\angle ONK\), \(\angle MNP\) and \(\angle LKI\)