Question

gi and jl are parallel lines. which angles are supplementary angles? ∠lkh and ∠ghk ∠lkh and ∠lkm ∠lkh and ∠jkm ∠lkh and ∠ihf

Explanation:

Step1: Recall the definition of supplementary angles

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

Step2: Analyze \(\angle LKH\) and \(\angle LKM\)

\(\angle LKH\) and \(\angle LKM\) form a linear pair. A linear pair of angles is supplementary.

Step3: Analyze \(\angle LKH\) and \(\angle GHK\)

Since \(JL\parallel GI\), \(\angle LKH=\angle GHK\) (alternate - interior angles). Their sum is not \(180^{\circ}\) unless each is \(90^{\circ}\) (not indicated).

Step4: Analyze \(\angle LKH\) and \(\angle JKM\)

\(\angle JKM\) and \(\angle LKH\) are vertical angles. Vertical angles are equal, and their sum is not \(180^{\circ}\) unless each is \(90^{\circ}\) (not indicated).

Step5: Analyze \(\angle LKH\) and \(\angle IHF\)

Since \(JL\parallel GI\), \(\angle LKH=\angle IHF\) (corresponding angles). Their sum is not \(180^{\circ}\) unless each is \(90^{\circ}\) (not indicated).

Answer:

\(\angle LKH\) and \(\angle LKM\)