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The word complementary in English means something that completes and brings perfection. In maths, two angles are said to be complementary when they add to give 90 degrees. That means these two angles together form a right angle.
Let ∠C =40 degree
∠D = 50 degree
Now ∠C + ∠D = (40 + 50 ) degree
= 90 degrees
Therefore, both angles C and D are complementary angles as they are making a total of 90 degrees.
Also, note that each angle of the complementary angles is called the “complement “ of the other angle.
If, ∠A + ∠B = 90 degrees
Then we can conclude that ∠A is the complement of ∠B and vice versa.
In the above diagram let ∠AOB = 60 degree and ∠BOC = 30 degree
∠AOB + ∠BOC = 90 degree which means they are complementary angles.
Two angles are said to be adjacent complementary if they have a common vertex and common arm and their sum is 90 degrees. In the above figure, both angles (∠AOB & ∠BOC ) are adjacent complementary as they have a common vertex (O) and common arm (OB).
Two angles are known as to be non – adjacent complementary angles if they don’t have a common vertex and common arm but their sum is 90 degrees.
∠AOB = 45 degrees and ∠CDE = 45 degrees.
∠AOB + ∠CDE = 90 degrees
In above figures, though the sum of both the angles is 90 degrees but these angles don’t have common vertex and common arm. So, they are Non –adjacent complementary angles.
Just subtract the angle from 90 degree to get its complement angle.
This means that, the complement of ∠x is ∠90 – x.
The formula becomes:
Complement ∠x = 90 – ∠x
Sol) Complement of angle 20 degree = ( 90 – 20 ) degree
= 70 degree
A 90-degree angle is known as right angle which we will find in many geometric shapes like square, boxes, cuboids, cubes, ramps etc. The two angles don’t have to be just next to each other to be complementary, but if they are, you will automatically come to know as they form a right angle.
There is a special relationship between all three angles of triangle too. We know that, when we add all angles of a triangle, they sum to 180 degrees. In a right-angled triangle, you already know that one of those angles is 90 degrees. That leaves 90 degrees to be distributed between the other two angles which means they are complementary.
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