Final answer:
Vertical angles are pairs of opposite angles made by the intersection of two lines. They are equal in measure, which can be justified by using a protractor to measure and confirm that angles in each pair are congruent.
Step-by-step explanation:
To illustrate vertical angles, start by drawing two intersecting lines using a ruler. The lines will form four angles. Label the pairs of opposite angles "Angle A" and "Angle B" for one pair and "Angle C" and "Angle D" for the other pair. Vertical angles are the angles that are opposite each other when two lines cross. Thus, Angle A and Angle B are one pair of vertical angles, and Angle C and Angle D are another pair.
According to the Vertical Angles Theorem, vertical angles are equal in measure. So, Angle A is equal to Angle B, and Angle C is equal to Angle D. This is because when two straight lines intersect, they create two pairs of vertical angles that share the same vertex, and the angles are congruent (have the same measure).
To justify that their measures are the same, we could use a protractor to measure the angles and confirm that Angle A and Angle B have equal measures, as do Angle C and Angle D. This is how the concept of vertical angles can be represented in a sketch and justified mathematically.