Exploring Adjacent Angles | Definition, Examples, and Properties

Adjacent angles Chapter 1 (p. 46)

Adjacent angles are a pair of angles that share a common vertex and a common side

Adjacent angles are a pair of angles that share a common vertex and a common side. In other words, they are angles that are side by side and have a common point. The shared side is typically a ray that forms the vertex of both angles.

Adjacent angles can either be adjacent on the same line or adjacent at a point. When they are adjacent on the same line, they are commonly referred to as linear pairs. In this case, the sum of the two adjacent angles will always be 180 degrees, as they form a straight line.

On the other hand, when adjacent angles share a common vertex at a point, they are known as a pair of vertical angles. Vertical angles are always congruent, meaning they have the same angle measurement. This is also known as the vertical angle theorem.

To illustrate this, let’s consider an example. Suppose we have two adjacent angles, angle A and angle B, sharing a common vertex at point O.

O
/ \
/ \
/ \
A——–B

In this case, angles A and B are adjacent angles. Their common vertex is point O, and their shared side is the ray extending from O towards A and B. The angles are side by side.

It is important to note the distinction between adjacent angles and non-adjacent angles. Non-adjacent angles do not share a common vertex or a common side and are not side by side. They could be on different lines or at distant points.

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