Question

which angles are supplementary to each other? select all that apply. ∠cfb and ∠ibj ∠fbe and ∠jbf ∠dea and ∠ced ∠fcg and ∠ebi

Explanation:

To determine which angles are supplementary, we use the definition of supplementary angles: two angles are supplementary if their sum is \(180^\circ\) (they form a linear pair or are same - side interior angles, etc., depending on the context of the lines).

Analyzing \(\angle CFB\) and \(\angle IBJ\)

• First, we need to check the relationship between these two angles. From the diagram, we can see the position of the lines and the angles. If the lines are parallel and there are transversals, or if they form a linear - pair - like situation. But in this case, by looking at the diagram (assuming the lines and angle positions), we find that \(\angle CFB\) and \(\angle IBJ\) are not supplementary.

Analyzing \(\angle FBE\) and \(\angle JBF\)

• A linear pair of angles is formed when two adjacent angles form a straight line. The sum of angles in a linear pair is \(180^\circ\). \(\angle FBE\) and \(\angle JBF\) form a linear pair (they are adjacent and their non - common sides form a straight line). So, \(m\angle FBE + m\angle JBF=180^\circ\), which means they are supplementary.

Analyzing \(\angle DEA\) and \(\angle CED\)

• \(\angle DEA\) and \(\angle CED\) form a linear pair. The non - common sides of these two adjacent angles form a straight line. So, \(m\angle DEA + m\angle CED = 180^\circ\), and they are supplementary.

Analyzing \(\angle FCG\) and \(\angle EBI\)

• By looking at the diagram (the position of the lines and the angles), we can see that \(\angle FCG\) and \(\angle EBI\) are equal (corresponding angles or alternate - interior angles, depending on the parallel lines and transversals). Their sum is not \(180^\circ\) (unless they are right angles, which there is no indication of), so they are not supplementary.

So the pairs of supplementary angles are \(\angle FBE\) and \(\angle JBF\), \(\angle DEA\) and \(\angle CED\).

Answer:

\(\angle FBE\) and \(\angle JBF\), \(\angle DEA\) and \(\angle CED\)