Understanding Adjacent Angles: Definition, Examples, and Properties

adjacent angles

Adjacent angles are a pair of angles that have a common vertex and a common side between them, but do not overlap

Adjacent angles are a pair of angles that have a common vertex and a common side between them, but do not overlap. In other words, they are side by side, with no space between them.

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

A——–B
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C——–D

In this diagram, let’s consider angle ABC and angle CBD. These two angles are adjacent angles because they share a common vertex (point B) and a common side (BC). They are side by side, with no overlapping.

Adjacent angles can have different measures depending on the specific geometric configuration. They can be complementary or supplementary angles.

Complementary adjacent angles: Two adjacent angles are complementary if their measures sum up to 90 degrees. For example, if angle ABC measures 50 degrees, then angle CBD must measure 40 degrees for them to be complementary.

Supplementary adjacent angles: Two adjacent angles are supplementary if their measures sum up to 180 degrees. For example, if angle ABC measures 120 degrees, then angle CBD must measure 60 degrees for them to be supplementary.

Adjacent angles are commonly found in geometric shapes, such as polygons and parallel lines. They help in identifying relationships between angles and solving angle-related problems.

When working with adjacent angles, it can be helpful to keep in mind the following:

1. Adjacent angles always share a common vertex and side.
2. Adjacent angles do not overlap.
3. The measures of adjacent angles can vary, but they can be complementary or supplementary depending on their sum.

I hope this explanation helps clarify the concept of adjacent angles. If you have any further questions or need additional assistance, feel free to ask!

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