Final answer:
A pair of vertical angles are opposite angles formed by two intersecting lines. Complementary angles add up to 90 degrees, while supplementary angles sum to 180 degrees. These concepts are key in understanding geometric relationships.
Step-by-step explanation:
To answer the student's questions:
A pair of vertical angles are the opposite angles formed by two intersecting lines. They are equal in measure. For instance, if two lines intersect and create angles A, B, C, and D, then angle A is vertical to angle C, and angle B is vertical to angle D.
A pair of complementary angles are two angles whose measures add up to 90 degrees. For example, if you have angles E and F, and if the measure of E is 60 degrees, then angle F would need to be 30 degrees for them to be complementary.
Lastly, a pair of supplementary angles are two angles whose measures add up to 180 degrees. If angle G is 110 degrees, then angle H must be 70 degrees for G and H to be supplementary.
These distinctions in angles are fundamental concepts in geometry, which is the branch of mathematics that deals with properties and relationships of points, lines, angles, and surfaces.