Chapter 12.1, Problem 2E

To determine

To State: The relationship between the measures of two vertical angles.

Answer to Problem 2E

The measures of two vertical angles are equal.

Explanation of Solution

Vertical angles are angles that are formed opposite to each other when two lines intersect at a point.

  

In the above figure, the two lines intersect at a point to form four angles $\angle 1,\angle 2,\angle 3,\angle 4$ . Among the four angles, $\angle 1$ and $\angle 3$ are vertical angles and their measures are equal. Similarly, $\angle 2$ and $\angle 4$ are vertical angles and their measures are equal too.

Therefore, it can be said that the measures of two vertical angles are equal.