Exercise 2 Page 483

Let's draw two intersecting lines and label the four angles that form around the point of intersection.

The first type of angles formed are two pairs of vertical angles. By the Vertical Angles Congruence Theorem, we know that such angles are congruent. The second type of angles formed are four linear pairs. By the Linear Pair Postulate we know that such angles are supplementary, which means they sum to $180^{\circ }.$