Adjacent angle

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An adjacent angle is one that shares a common vertex and side with another angle, that is, they are consecutive angles. In turn, both angles are supplementary, that is, they form a straight angle of 180º (sexagesimal degrees) or π radians.

In simple terms, two angles are adjacent when they are consecutive and supplementary at the same time or, viewed differently, they are a particular category of consecutive angles.

It is also worth noting that those sides that the adjacent angles do not have in common are two rays that go in opposite directions. That is, looking at the image below (where ∝ and β are adjacent), both rays start from point B, but one passes through point A and the other through point D.

Adjacent angles

Adjacent angles are part of an angle category based on their position relative to another angle.

It should be remembered that an angle is an arc formed by the crossing of two rays, lines or segments.

A fact to observe is that two adjacent angles, having to be supplementary, must necessarily measure less than 180º. That is, they are convex angles that can be acute (less than 90º), straight (90º) or obtuse (between 90º and 180º).

Similarly, a concave angle, which measures more than 180º, cannot have an adjacent angle.

Examples of adjacent angles

Let's look at some examples of adjacent angles:

  • The interior and exterior angles that share the same vertex in a triangle are adjacent angles.

For example, in the image above, we see three pairs of adjacent angles since it is true that: ∝ + d = β + e = γ + h = 180º.

  • To mention a less abstract example, let's imagine that we go to the beach and set up an umbrella. The angles that are formed between the object and the ground, both towards its right side and its left side, are adjacent (We are assuming that the surface of the beach is flat).

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