If Two Angles Are Supplementary

The supplementary bending is i with which a direct angle is formed. That is, ii angles are supplementary if their sum is 180º (sexagesimal degrees) or π radians.

In the lower graph, α and β are supplementary angles (108.9º + 71.1º = 180º).

To discover the supplementary angle of an bending that measures xº nosotros only calculate the difference of 180º minus xº. Likewise, if the bending measure were in radians, we would subtract π – 10 (all in radians).

The supplementary angle is one of the classifications of the angles according to the outcome of their sum with some other bending.

It is worth mentioning that ii supplementary angles tin can be consecutive (as in the image above), just this is non always the case. In the lower image we see two non-consecutive supplementary angles (98.5º + 81.5º = 180º).

It should likewise exist remembered that an bending is an arc formed by the intersection of two lines, rays or segments.

Supplementary Angle Examples

Let'due south wait at some examples of supplementary bending. For example, if bending x measures 130º, its supplementary bending measures 50º (180º-130º).

Too, 2 angles that are right or that measure 90º are supplementary to each other, and an angle greater than 180º. For instance, one measuring 230º has no supplementary angle.

Another additional point to find is that a supplementary angle always measures less than 180º. That is, it cannot exist a concave angle (greater than 180º).

As well, it is worth noting that ii astute angles (less than 90º) cannot exist supplementary.

To refer to a more graphic case, if we draw the two diagonals of a quadrilateral, for instance, a rectangle, at the intersection, those adjacent angles are supplementary. Thus, we run across in the image below that information technology is true that 118.1º + 61.9 = 180º.

Similarly, another particular case is that of triangles where each interior angle is supplementary to its respective outside angle at the aforementioned vertex. For example, in the image below information technology is truthful that:

180º = ∝ + d = β + e = h + γ