Question

topic: properties of angles
progress:
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
which sets of angles listed are complementary in this diagram?
○ ∠aeg and ∠ceg, ∠ceg and ∠ceb
○ ∠aeg and ∠aed, ∠fed and ∠deb
○ ∠aef and ∠fed, ∠aeg and ∠ceg
○ ∠aef and ∠fed, ∠fed and ∠deb

Explanation:

Step1: Recall definition of complementary angles

Complementary angles add up to 90°.

Step2: Analyze the diagram

In the given diagram, we look for pairs of angles that form a right - angle. We know that $\angle AEB = 180^{\circ}$ and $\angle CED=180^{\circ}$, and $\angle AEC = 90^{\circ}$, $\angle BED = 90^{\circ}$.

Step3: Check each option

• Option 1: $\angle AEG+\angle CEG$ may not be 90° always, and $\angle CEG+\angle CEB$ is not 90°.
• Option 2: $\angle AEG+\angle AED$ is not 90°, $\angle FED+\angle DEB$ is not 90°.
• Option 3: $\angle AEF+\angle FED$ forms a right - angle (assuming $EF$ is positioned such that it divides $\angle AED$ appropriately), and $\angle AEG+\angle CEG$ forms a right - angle as $\angle AEC = 90^{\circ}$.
• Option 4: $\angle AEF+\angle FED$ forms a right - angle, but $\angle FED+\angle DEB$ is not 90°.

Answer:

$\angle AEF$ and $\angle FED$, $\angle AEG$ and $\angle CEG$