The vertex is the corner of the angle, where the two segments or rays or lines meet. In this case, the vertex is point D.
Give four names for ∠1 (aside from ∠1, obviously).
Rather than name it by number, we can use the points to name the angle, making sure that the vertex is always in the middle. We could name it ∠BDE, ∠EDB, ∠BDF, and ∠FDB. They all represent the same angle. Note that every one of them has D in the middle.
Name an angle adjacent to ∠1.
Adjacent angles share a side and a vertex. ∠BDC (which can also be written ∠CDB) is adjacent to ∠1.
Name a pair of vertical angles.
Vertical angles are just opposite each other when two segments intersect. Angles ∠FEG (also written ∠GEF) and ∠BED (also known as ∠DEB, ∠BEC, ∠CEB, ∠AED, ∠DEA, ∠AEC, or ∠CEA) are vertical angles. Another pair of vertical angles is ∠FEB (which is the same as ∠FEA, ∠BEF, and ∠AEF) and ∠GED (also ∠DEG, ∠GEC, or ∠CEG). Clearly, these angles love alter egos.