Understanding Adjacent Angles: Definitions, Classification, and Examples

Adjacent Angles

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

Adjacent angles are a pair of angles that have a common side and a common vertex but do not overlap. In other words, they are angles that are positioned side by side and share one side with each other.

To better understand adjacent angles, it’s important to know some basic terms related to angles:

1. Angle: An angle is formed when two rays, called sides, share a common endpoint, known as the vertex.

2. Vertex: The vertex of an angle is where the two sides of the angle meet.

3. Side: The sides of an angle are the two rays that extend from the vertex in opposite directions.

Now, let’s take a look at an illustration to help visualize adjacent angles.

A
/\
/ \
a / \ b
/ \
/________\
B c

In the figure above, angle A and angle c share a common vertex (B) and a common side (BC). Therefore, angle A and angle c are adjacent angles.

Adjacent angles can have different measurements and can be classified into three categories:

1. Adjacent supplementary angles: When the sum of the angles is 180 degrees, they are called adjacent supplementary angles. This means that the two angles form a straight line when combined.

2. Adjacent complementary angles: When the sum of the angles is 90 degrees, they are called adjacent complementary angles. This means that the two angles form a right angle when combined.

3. Adjacent angles with no specific relationship: When the sum of the angles is neither 180 degrees nor 90 degrees, the adjacent angles have no specified relationship regarding their measurement.

In summary, adjacent angles are a pair of angles that have a common side and a common vertex without overlapping. They can be adjacent supplementary angles, adjacent complementary angles, or adjacent angles with no specific relationship.

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