Question

which sets of angles listed are complementary in this diagram? ∠aeg and ∠aed , ∠fed and ∠deb ∠aef and ∠fed , ∠aeg and ∠ceg ∠aef and ∠fed , ∠fed and ∠deb ∠aeg and ∠ceg , ∠ceg and ∠ceb

Explanation:

Step1: Recall complementary - angles definition

Two angles are complementary if the sum of their measures is 90°.

Step2: Analyze each option

• Option 1: $\angle AEG$ and $\angle AED$: $\angle AEG+\angle AED

eq90^{\circ}$.

• Option 2: $\angle AEF$ and $\angle FED$: $\angle AEF+\angle FED = \angle AED$. Since $\angle AED = 90^{\circ}$, $\angle AEF$ and $\angle FED$ are complementary. Also, $\angle AEG$ and $\angle CEG$: $\angle AEG+\angle CEG=\angle AEC = 180^{\circ}$ (not complementary).
• Option 3: $\angle AEF$ and $\angle FED$ are complementary as $\angle AEF+\angle FED = 90^{\circ}$, but $\angle FED$ and $\angle DEB$: $\angle FED+\angle DEB

eq90^{\circ}$.

• Option 4: $\angle AEG$ and $\angle CEG$ are supplementary ($\angle AEG+\angle CEG = 180^{\circ}$), not complementary. And $\angle CEG$ and $\angle CEB$: $\angle CEG+\angle CEB

eq90^{\circ}$.

Answer:

$\angle AEF$ and $\angle FED$