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The sum of the two angles’ measurements determines the complement and supplement of the two angles’ measurements. This is referred to as a complementary angle pair when the sum of the two angles is equal to the measurement of the right angle in the pair of angles.
Complementary angles are pairs of angles with a sum of 90 degrees. Always keep in mind that complementary angles occur in pairs when discussing them. One angle is the counterpart of the other. Although a right angle is 90 degrees, it cannot be considered complimentary because it does not occur in pairs. There is only one angle present. Three or more angles whose sum equals 90 degrees cannot be considered complementary angles. Complementary angles have always positive measurements. It consists of two acute angles measuring less than 90 degrees.
What is the complementary angle?
The sum of two angles is considered to be complementary if the sum of the angles equals 90 degrees. To put it another way, when two complementary angles are combined, they make a right angle (see figure) (90 degrees). A pair of angles 1 and 2 are complementary if the sum of their respective angles is equal to 90 degrees (that is, if angle 1 plus angle 2 equals 90°). As a result, angle 1 and angle 2 are referred to as complements of each other.
In the illustration below, 60° plus 30° equals 90°. Following the “Definition of Complementary Angles,” it may be concluded that these two angles are complementary. Each of the complementary angles is referred to as the “complement” of the other angle in the pair. Here,
The angle 60° is the complement of the angle 30°.
30° is complimentary to 60°.
Adjacent complementary angles
When the total of two angles is equal to the measurement of a right angle, the pair of angles is referred to as the complementary angle (or the complementary triangle). Complementary angles in geometry are classified into two categories, which are as follows:
Angles that are adjacent and complementary to one another
Complementary Angles that are not contiguous to one another
Angles that are adjacent and complementary: The term “adjacent complementary angles” refers to two complementary angles that share a shared vertex and a common arm. In the illustration below, the angles COB and AOB are neighbouring angles because they share a common vertex (“O”) and a shared arm (“OB”) The angles COB and AOB add up to 90 degrees, as shown by the equation COB + AOB = 70°+20° = 90°. As a result, these two angles are complementary angles that are next to one another.
Non-adjacent complementary angles
Non-adjacent Complementary Angles: Two complementary angles that are NOT next to one another are referred to as non-adjacent complementary angles in mathematics. In the diagram below, the angles ABC and PQR are not neighbouring since they do not share a common vertex or a common arm. Further to this, they sum up to 90 degrees, as in AB+ PQR = 50°+ 40° =90°. As a result, these two angles are complementary angles that are not contiguous. In the case of non-adjacent complementary angles that are not neighbouring, they combine to form a right angle.
Important points
Complementary angles are defined as those in which the sum of the two angles equals or exceeds 90 degrees. When two angles are 50 degrees and 40 degrees apart, these angles are complementary since the sum of these angles is 90 degrees: 50 + 40 = 100 ° angle of complementarity.
When two angles are complementary to each other, angle one is referred to as the complement of angle 2, and angle two is referred to as the complement of angle one.
It makes no difference where the angles are located. The only requirement for a pair of angles to be considered complimentary is that the total of their respective angles should be 90 degrees.
It is possible for two sharp angles to be complementary.
It is impossible for two obtuse to be complementary.
It is impossible for one obtuse angle and one acute angle to be complimentary.
Because one right angle is equal to 90 degrees, two right angles cannot be complementary to each other.
Properties of complementary angles
When the sum of two angles equals 90 degrees, they are said to be complimentary.
They can either be adjacent or non-adjacent to one another.
Even though the sum of three or more angles is 90 degrees, they cannot be considered complementary.
When two angles are complementary to one another, one angle is referred to as the “complement” or “complement angle” of the other.
A right-angled triangle has two acute angles that are complementary to one another.
Conclusion
Complementary angles are pairs of angles with a sum of 90 degrees. A right angle is 90 degrees but cannot be considered complimentary because it does not occur in pairs. Three or more angles whose sum equals 90 degrees cannot be complementary abundantly. Complementary angles are defined as those in which the sum of the two angles equals or exceeds 90 degrees. They can either be adjacent or non-adjacent to one another. In the diagram below, the angles ABC and PQR are not neighbouring since they do not share a common vertex or a common arm.
