Complementary Angles

Complementary angles are two angles whose sum remains equivalent to 90 degrees. These two angles are supposed to complement each other and form a right triangle. They also happen to be congruent if they complement each other. Let’s have a deep insight into the concept of complementary angles, learning more about its uses, properties, etc.

Complementary Angles:

Two angles whose sum equals 90 degrees are called complementary angles. For example, 55 & 35 degrees, 45 & 45 degrees, 30 & 60 degrees, and other similar angles can be called complementary angles. Therefore, any angle X and angle Y are said to be complementary when their measurement’s sum is equivalent to the measurement of a right angle, i.e., ANGLE X + ANGLE Y = 90 degrees. Hence, x and y angles will be identified as complements of each other. Let’s understand complementary angles through some examples.

From the listed measurements, identify complementary angles in pairs.

In the given list, Angle A (76 degrees) and Angle G (14 degrees) form a 90 degrees angle that certifies them as complementary angles. Similarly, Angle C (52 degrees) and Angle F (38 degrees) can be complementary angles.

In both the cases, complements are as follows:

a) Angle A (76 degrees) is a complement of Angle G (14 degrees), and Angle G (14 degrees) is a complement of Angle A (76 degrees).

b) Angle C (52 degrees) is a complement of Angle F (38 degrees) and vice-versa.

Properties of complementary angles

1) When two angles add up to 90 degrees and make a right angle, they are known as complementary angles.

2) You can remember C for complement and C for the corner of a right angle.

3) Complementary angles can be either adjacent angles or non-adjacent angles.

4) Only two angles can be complementary. There can never be three or more angles described as complementary angles despite their sum being 90°.

5) The complementary angles can be joined together to form a right-angle shape.

6) Right-angled triangle may have two complementary acute angles. Acute angles are angles whose measurements are less than 90 degrees.

7) Complementary angles need not be a part of the same figure. They can coexist in different figures instead of just one. Hence, one must only ensure that their sum equals 90 degrees, not the other factors.

8) There exists numerous uses of complementary angles. It helps us find unknown angles and acts as a problem-solving concept in geometry and trigonometry.

Complementary Angles Theorem

The theorem of complementary angles states two things which are as follows:

1. Two angles are said to be congruent if they are complements of each other.

2. Two angles will also be congruent if they complement two other congruent angles.

Types Of Complementary Angles

There are two types of complementary angles in geometry. They are as follows:

• Adjacent Complementary Angle

Any two angles having a common vertex and a common arm whose sum is 90 degrees are known as adjacent complementary angles. Both the angles will always be acute and form an L shape together.

• Non-Adjacent Complementary Angle

Any two angles that are not placed side by side, i.e., two complementary angles without a common arm or vertex, are called non-adjacent complementary angles. They always form a right angle when put together on the surface.

Conclusion

When the sum of two angles equals 90°, they are called complementary angles. Complementary angles are of two types: Adjacent Complementary Angle and Non-adjacent Complementary Angle. If two angles complement each other, they can also be called congruent. Besides, complementary angles need not be a part of the same figure, and they can exist in different figures.