Question

When two lines intersect at one point, how many pairs of vertical angles are formed? Explain your answer.

Short answer

Two pairs of vertical angles are formed.

Step-by-step solution

Step 1. Given Information.

Two lines intersect at one point.

Step 2. Explanation.

Two angles are called a pair of vertically opposite angles, if their arm forms two pairs of opposite rays. For example, let two lines AB and CD intersect at O, then $\angle AOD\text{and}\angle COB$ form a pair of vertically opposite angles and $\angle AOC\text{and}\angle BOD$ form another pair of vertically opposite angles.

Step 3. Conclusion.

When two lines intersect at one point, two pairs of vertically opposite angles are formed.