1. **State the problem:** Identify which pairs of angles are supplementary, meaning their measures add up to $$180^\circ$$. 2. **Recall that supplementary angles** are two angles whose sum is $$180^\circ$$. 3. **Analyze the given pairs:** - $$\angle LMO$$ and $$\angle NMO$$: Since points L, M, O, and N are on or around the intersecting lines, and M is the vertex, if $$\angle LMO$$ and $$\angle NMO$$ are adjacent and form a straight line, they are supplementary. - $$\angle LMO$$ and $$\angle KJH$$: $$\angle KJH$$ involves points K, J, and H on different lines not sharing vertex M, so unlikely to be supplementary with $$\angle LMO$$. - $$\angle LMO$$ and $$\angle NMJ$$: $$\angle NMJ$$ shares vertex J, different from vertex M, so likely not supplementary with $$\angle LMO$$. - $$\angle LMO$$ and $$\angle IJM$$: $$\angle IJM$$ has vertex J, different from M, so likely not supplementary. 4. **Confirm by line geometry:** Since $$\angle LMO$$ and $$\angle NMO$$ share vertex M and are adjacent on the intersecting lines, they form a linear pair and thus are supplementary. 5. **Final answer:** The supplementary pair is $$\angle LMO$$ and $$\angle NMO$$.