Question

which angles are supplementary angles?
∠ihe and ∠ghj ∠ihe and ∠deh
∠feh and ∠fec ∠ghj and ∠fec

Explanation:

Step1: Recall the definition of supplementary angles

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

Step2: Analyze $\angle FEH$ and $\angle FEC$

Since $\angle FEH$ and $\angle FEC$ form a linear - pair (they are adjacent angles and their non - common sides form a straight line). By the linear - pair postulate, if two angles form a linear pair, then they are supplementary. So, $\angle FEH+\angle FEC = 180^{\circ}$.

Step3: Analyze $\angle IHE$ and $\angle GHJ$

$\angle IHE$ and $\angle GHJ$ are vertical angles. Vertical angles are equal, but their sum is not necessarily $180^{\circ}$ (unless each is $90^{\circ}$).

Step4: Analyze $\angle IHE$ and $\angle DEH$

These are alternate interior angles (assuming $DF\parallel GI$). Alternate interior angles are equal (if the lines are parallel), and their sum is not $180^{\circ}$ (unless each is $90^{\circ}$).

Step5: Analyze $\angle GHJ$ and $\angle FEC$

There is no geometric relationship (such as linear - pair, etc.) that would make their sum $180^{\circ}$.

Answer:

$\angle FEH$ and $\angle FEC$