Question

which angles are adjacent to each other? select all that apply. ∠edf and ∠fdg ∠iae and ∠ade ∠aeb and ∠bec ∠aeb and ∠fdg

Explanation:

To determine adjacent angles, we use the definition: two angles are adjacent if they share a common side and a common vertex, and their non - common sides are on either side of the common side.

Analyze \(\angle EDF\) and \(\angle FDG\)

• Common vertex: Both angles have vertex \(D\).
• Common side: They share the side \(DF\).
• Non - common sides: The non - common sides \(DE\) (of \(\angle EDF\)) and \(DG\) (of \(\angle FDG\)) are on either side of \(DF\). So, \(\angle EDF\) and \(\angle FDG\) are adjacent.

Analyze \(\angle IAE\) and \(\angle ADE\)

• Common vertex: The vertex of \(\angle IAE\) is \(A\) and the vertex of \(\angle ADE\) is \(D\). Since they do not share the same vertex, they are not adjacent.

Analyze \(\angle AEB\) and \(\angle BEC\)

• Common vertex: Both angles have vertex \(E\).
• Common side: They share the side \(EB\).
• Non - common sides: The non - common sides \(EA\) (of \(\angle AEB\)) and \(EC\) (of \(\angle BEC\)) are on either side of \(EB\). So, \(\angle AEB\) and \(\angle BEC\) are adjacent.

Analyze \(\angle AEB\) and \(\angle FDG\)

• Common vertex: The vertex of \(\angle AEB\) is \(E\) and the vertex of \(\angle FDG\) is \(D\). Since they do not share the same vertex, they are not adjacent.

The correct adjacent angle pairs are \(\angle EDF\) and \(\angle FDG\), \(\angle AEB\) and \(\angle BEC\).

Answer:

\(\angle EDF\) and \(\angle FDG\), \(\angle AEB\) and \(\angle BEC\)