In the given diagram, we are tasked with finding the angle congruent to ∠DEA, other than itself.

Analysis:

• ∠DEA is an angle formed by the intersection of several lines at point E.
• From the diagram, ∠DEA is adjacent to ∠AEB and ∠CEA, as they share vertex E.

The key here is identifying angles based on the fact that vertical angles (or opposite angles) are always congruent when two lines intersect. Vertical angles are formed when two lines cross, and they are directly opposite each other.

Step-by-Step Solution:

• ∠DEA and ∠CEB are vertical angles because they are on opposite sides of the intersection of the two lines through E.
• Since vertical angles are always congruent, ∠DEA ≅ ∠CEB.

Thus, the angle congruent to ∠DEA, other than itself, is ∠CEB.

Would you like further clarification or details on any part of this explanation?

Here are 5 related questions:

1. What are complementary and supplementary angles?
2. How can you determine the sum of angles in a triangle?
3. What is the property of alternate interior angles in parallel lines?
4. How are adjacent angles defined, and when are they complementary?
5. What is the significance of corresponding angles in geometry?

Tip: When dealing with intersecting lines, always check for vertical angles—they are guaranteed to be congruent.