Adjacent Angles
Adjacent angles are a pair of angles that have a common vertex and a common side between them
Adjacent angles are a pair of angles that have a common vertex and a common side between them. In other words, adjacent angles share a side and a vertex, but do not overlap or intersect.
The common side of adjacent angles acts as a ray that separates the two angles. This ray is known as the common side or the arms of the adjacent angles. The vertex of adjacent angles is the point where the two arms meet.
For example, if we have two lines intersecting each other, we can form adjacent angles at the point of intersection. If we label the intersecting lines as line l and line m, and the point of intersection as point P, then we can have adjacent angles such as ∠APB and ∠BPC.
Adjacent angles can have different attributes and relationships. They can be complementary, supplementary, or have no special relationship at all.
Complementary adjacent angles add up to 90 degrees. For instance, if one angle measures 30 degrees, the adjacent angle will measure 60 degrees for the two angles to be complementary.
Supplementary adjacent angles add up to 180 degrees. For example, if one angle measures 120 degrees, the adjacent angle will measure 60 degrees to make the two angles supplementary.
Adjacent angles can also form linear pairs when they are adjacent, supplementary, and lie on the same line. In a linear pair, the sum of the two angles is always 180 degrees.
It is important to distinguish adjacent angles from other types of angles like vertical angles, which are opposite each other when two lines intersect. Unlike adjacent angles, vertical angles are not next to each other but are instead across from each other.
In summary, adjacent angles are a pair of angles that share a common vertex and a common side between them. They can be complementary, supplementary, or form a linear pair depending on their angle measures and relationship.
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