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Vertical Angles in Geometry

What are Vertical Angles?

Vertical angles are pairs of opposite angles that are formed by two intersecting lines. Vertical angles have the same vertex and are always congruent (equal in measure). In other words, vertical angles are equal in measure.

How to Identify Vertical Angles

Vertical angles are easy to identify. They are opposite angles that are formed when two lines intersect. If two lines intersect at a point, then the angles opposite each other are vertical angles.

Relationships of Vertical Angles

Vertical angles are always congruent. That means that they are equal in measure. In addition, when two lines intersect, the angles are complementary. That means that the sum of the angles is 180 degrees.

Examples of Vertical Angles

The following figure shows an example of two intersecting lines and the vertical angles that are formed by them.

Vertical Angles Example

In the figure above, the angles A and B are vertical angles. The angles C and D are also vertical angles. All the angles are congruent, that is, they all have the same measure.

Adjacent Angles

Adjacent angles are angles that have a common side and a common vertex. Adjacent angles are not vertical angles, but they are related. The sum of adjacent angles, such as angles A and B in the figure above, is equal to 180 degrees.

Practice Problems

1. Name the vertical angles in the following figure.

Vertical Angles Practice Problem

Answer: Angles A and B, and angles C and D.

2. Are angles A and C adjacent angles?

Answer: No, angles A and C are not adjacent angles.

3. Find the measure of angle B.

Answer: The measure of angle B is 90 degrees.

4. Are angles A and B complementary angles?

Answer: Yes, angles A and B are complementary angles.

5. Find the measure of angle C.

Answer: The measure of angle C is also 90 degrees.

Summary

In this article, we have discussed vertical angles in geometry. We have seen that vertical angles are equal in measure and that they are complementary angles. We have also seen that adjacent angles are not vertical angles, but they are related. Finally, we have seen some practice problems to test our understanding of vertical angles.

FAQ

What are Vertical Angles?

Vertical angles are angles that are opposite each other and have the same measure. They are formed when two lines cross.

How are Vertical Angles Named?

Vertical angles are named by their corresponding vertex points. For example, vertical angles A and B are named ?A and ?B.

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