1. The problem asks to compile a list of angle properties and characteristics, focusing on symmetry and angle properties. 2. Angle properties include: - Complementary angles: Two angles whose sum is $90^\circ$. - Supplementary angles: Two angles whose sum is $180^\circ$. - Vertically opposite angles: When two lines intersect, opposite angles are equal. - Adjacent angles: Two angles that share a common arm and vertex. - Angles on a straight line: Sum to $180^\circ$. - Angles around a point: Sum to $360^\circ$. - Alternate interior angles: Equal when two parallel lines are cut by a transversal. - Corresponding angles: Equal when two parallel lines are cut by a transversal. - Co-interior angles: Sum to $180^\circ$ when two parallel lines are cut by a transversal. 3. Symmetry in angles often relates to equal angles formed by symmetrical figures or lines. 4. Diagrams are essential for visualizing these properties but cannot be included in this text response. 5. For example, vertically opposite angles formed by intersecting lines are equal: $$\angle A = \angle C, \quad \angle B = \angle D$$ 6. Similarly, complementary angles satisfy: $$\angle X + \angle Y = 90^\circ$$ 7. Supplementary angles satisfy: $$\angle M + \angle N = 180^\circ$$ This list covers the main angle properties relevant to symmetry and angle relationships.