## Adjacent angles Chapter 1 (p. 46)

### Adjacent angles are a pair of angles that have a common vertex and a common side

Adjacent angles are a pair of angles that have a common vertex and a common side. These angles are formed when two lines intersect or when a line intersects with a transversal line.

To understand adjacent angles better, let’s consider the following diagram:

A O

/ /

/ /

B C

In the diagram, line AB and line AC intersect at point A. We can see that there are two angles formed at point A – angle AOB and angle AOC. These angles are adjacent angles since they share a common vertex (A) and a common side (AO).

It is important to note that adjacent angles can either be complementary, supplementary, or neither.

1. Complementary Adjacent Angles: Complementary adjacent angles are two angles whose measures add up to 90 degrees. For example, if angle AOB measures 60 degrees, then angle AOC will measure 30 degrees, and together they form a pair of complementary adjacent angles.

2. Supplementary Adjacent Angles: Supplementary adjacent angles are two angles whose measures add up to 180 degrees. For instance, if angle AOB measures 120 degrees, then angle AOC will measure 60 degrees, and together they form a pair of supplementary adjacent angles.

3. Neither Complementary nor Supplementary: There can be cases where adjacent angles do not add up to 90 degrees or 180 degrees. In such scenarios, they are neither complementary nor supplementary.

Adjacent angles can also help us identify various properties and relationships between angles. For instance:

– Vertically Opposite Angles: When two lines intersect, the pair of opposite angles formed are called vertically opposite angles. These angles are equal in measure. In the diagram, angle AOB and angle COB are vertically opposite angles.

– Linear Pair: When two adjacent angles are formed by the intersecting lines, they are called a linear pair of angles. Linear pairs always add up to 180 degrees. In the diagram, angle AOB and angle AOC form a linear pair.

Understanding adjacent angles is crucial in solving geometric problems and proofs. So, it’s important to practice identifying and working with adjacent angles to develop a strong foundation in geometry.

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