Understanding Adjacent Angles | Definition, Properties, and Examples

Adjacent Angles

Adjacent angles are two angles that share a common side and a common vertex, but do not overlap

Adjacent angles are two angles that share a common side and a common vertex, but do not overlap. They are side by side, with the shared side forming a line between them. In other words, the interior of one angle does not intersect with the interior of the other angle.

When two lines intersect, four angles are formed at the point of intersection. Adjacent angles are two of these angles that are next to each other.

For example, let’s consider two lines, line AB and line CD, intersecting at point P. There will be four angles formed: angle APD, angle BPC, angle APB, and angle CPD.

If we focus on angle APD, the adjacent angles to it would be angle BPC and angle APB. These two angles share a common side (line PB) and a common vertex (point P) with angle APD, but they do not overlap with it.

Adjacent angles can have different measures and classifications. They can be complementary, supplementary, congruent, or even have no special relationship. It depends on the specific measurements and relationships between the angles.

Complementary adjacent angles: Two angles that add up to 90 degrees are called complementary angles. If the adjacent angles both have measures that add up to 90 degrees, they are considered complementary adjacent angles.

Supplementary adjacent angles: Two angles that add up to 180 degrees are called supplementary angles. If the adjacent angles both have measures that add up to 180 degrees, they are considered supplementary adjacent angles.

Congruent adjacent angles: Two angles that have the same measure are called congruent angles. If the adjacent angles have the same measure, they are considered congruent adjacent angles.

It’s important to note that adjacent angles can only be formed when lines intersect. If the lines are parallel, there will be no intersection and hence no adjacent angles.

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