Question

which sets of angles listed are complementary in this diagram?

∠aef and ∠fed, ∠fed and ∠deb
∠aeg and ∠aed, ∠fed and ∠deb
∠aeg and ∠ceg, ∠ceg and ∠ceb
∠aef and ∠fed, ∠aeg and ∠ceg

Explanation:

Step1: Recall the definition of complementary angles

Complementary angles are two angles whose sum is \(90^{\circ}\).

Step2: Analyze each option

• For \(\angle AEF\) and \(\angle FED\):

Since \(AE\perp ED\) (as \(AB\) and \(CD\) are perpendicular at \(E\)), \(\angle AED = 90^{\circ}\). So \(\angle AEF+\angle FED=\angle AED = 90^{\circ}\).

• For \(\angle AEG\) and \(\angle CEG\):

Since \(AE\perp CE\) (as \(AB\) and \(CD\) are perpendicular at \(E\)), \(\angle AEC = 90^{\circ}\). So \(\angle AEG+\angle CEG=\angle AEC = 90^{\circ}\).

Answer:

\(\angle AEF\) and \(\angle FED\), \(\angle AEG\) and \(\angle CEG\)