Supplementary Angles- Everything you need to know!

The word "supplementary" is derived from two Latin words, "Supplere" and "Plere," where "Supplere" means "supply" and "Plere" means "fill." As a result, "supplementary" refers to "anything that is added to a thing in order to complete it." Likewise, supplementary angles, which are a combination of two angles that, when combined, make a straight angle (180 degrees) when they are joined. These two perspectives are unquestionably considered to be complementary to one another.


Angle measurement and angle discovery are two of the most commonly performed tasks in Geometry. However, in order to do so, you must first have a solid understanding of geometrical principles. In this lesson, we will delve into the world of supplementary angles, which have a wide range of applications in the solution of a wide range of geometry issues.




When are two angles called supplementary?


Two angles are considered supplementary, if their sum is equal to 180 degrees. When all of the supplementary angles are added together, they make a straight angle (180 degrees). In other words, if Angle 1 + Angle 2 = 1800, then angle 1 and angle 2 are supplementary angles.




Adjacent and Non-Adjacent Supplementary Angles


Supplementary angles can be either adjacent or non-adjacent to one another. As a result, additional angles can be divided into two categories. Each of these sorts of extra angles is discussed in greater detail below.





Adjacent Supplementary Angles


An adjacent supplementary angle is defined as a pair of adjoining supplementary angles that share a shared vertex and a common arm.




Non-adjacent Supplementary Angles


It is referred to as non-adjacent supplementary angles when two supplementary angles are not adjacent to one another.




Supplementary V/S Complementary Angles


Crossroads is one of the most common real-time applications for supplementary and complementary angles, which are angles that exist in pairs and add up to 180 and 90 degrees, respectively. 




Is it possible to calculate the Supplement of an Angle?


In cases where the sum of two pairs of angles equals 180°, we refer to that pair of angles as supplements to one another. The sum of two supplemental angles equals 180 degrees, and each of them is referred to as a "supplement" of the other in this context. As a result, finding the supplement of an angle is as simple as subtracting it from 180 degrees. This means that the x° supplement is equal to (180 - x)°.


For example, the supplement of 68° can be derived by subtracting it from 180° in the formula. As a result, the supplement is (180- 68)° = 112°.




Congruent Supplementary Angles


Congruent angles are those that have the same measure as one another. As a result, all angles with the same measure will be referred to as congruent angles. Their presence may be found almost anywhere, for example, in equilateral triangles, isosceles triangles, and whenever two parallel lines are intersected by a transversal.


Congruent angles are defined as follows in mathematics: "angles that are equivalent in measure are referred to as congruent angles." In other terms, equal angles are angles that are congruent with one another. In mathematics, it is denoted by the symbol ≅, therefore if we wish to convey the fact that ∠A is congruent to ∠X, we will write it as ∠A ≅ ∠X.


Supplementary angles are those whose sum is greater than 180 degrees. Regardless of whether or not they are adjacent angles, angles that are supplemented to the same angle are congruent angles, according to this theorem.




Angles that form a linear pair are supplementary- Proof with Explanation!


It is possible to generate linear pairs of angles when two lines intersect at a single point, but this is rare. It is said that the angles are linear if they are next to each other after the two lines intersect at their junction point. 


It is now necessary to demonstrate that the angles forming a linear pair are supplementary, that is, that the total of the angles comprising a linear pair equals 180°, and that this is true. Let's make a diagram to help us understand the idea more clearly. For simplicity, assume that AB and CD are two lines that meet at the point O.


As we can see, ∠AOC and ∠BOC are immediately adjacent to one another following the intersection of two lines, as shown in the diagram. As a result, the angles ∠AOC and ∠BOC form a linear pair.


Based on the diagram, we may conclude that the sum of ∠AOC and ∠BOC equals the sum of ∠AOB.


As a result, ∠AOC and ∠BOC are equal to AOB.


This is because ∠AOB is an angle formed by two lines AB, and as such, it is a straight angle. As a result, ∠AOB equals 180.


We now have ∠AOC and ∠BOC=90, respectively.


This means that ∠AOC and ∠BOC are complementary angles because their sum equals 180, as seen in the diagram. Because they were linear pairs of angles, we may argue that the angles that make up a linear pair are supplementary to one another.


As a result, the assertion is correct.




Acute Angles



The point at which two rays intersect is referred to as the vertex. This angle is referred to as an acute angle when it is less than 90° in measurement. In addition, when a right angle is divided in half, it produces two acute angles as a result.




Obtuse Angles



Obtuse angles are defined in Geometry as angles with measures more than 90° but less than 180°. In other words, an obtuse angle is defined as an angle with a measure greater than 90° but less than 180°.

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