Question

which angles are supplementary to ∠bed? select all that apply.

Explanation:

Step1: Recall supplementary - angle definition

Two angles are supplementary if their sum is 180 degrees.

Step2: Analyze adjacent - angles to ∠BED

∠BED and ∠BEC form a linear - pair. A linear - pair of angles is supplementary. So ∠BEC is supplementary to ∠BED.

Step3: Analyze non - adjacent supplementary angles

We know that the sum of angles around a point is 360 degrees. If we consider the angles at point E, and since ∠BED+∠DEA + ∠AEC+∠CEB = 360 degrees and ∠BED+∠BEC = 180 degrees, also ∠BED+∠DEA+∠AEC = 180 degrees. So ∠DEA and ∠CEA are also supplementary to ∠BED.

Answer:

∠BEC, ∠DEA, ∠CEA