About Complementary & Supplementary Angles
- Introduction
- Complementary angles
- Supplementary angles
- The methodology to find supplementary and complementary angles For complementary angles
- For complementary angles
- For supplementary angles
- Some key points
- Rapid recall
- Solved Examples: Complementary Angles and Supplementary Angles
- Frequently Asked Questions
Introduction
Complementary angles and supplementary angles are based on the sum of two angles.
What are Complementary angles?
Complementary angles are those whose sum is always 90 degrees.
In this figure, \(\angle\)AOB and \(\angle\)BOD are complementary angles, as the sum of these two angles is 30 + 60 = \(90^\circ\).
What are Supplementary angles?
Supplementary angles are those whose sum is always 180 degrees.
In this figure, \(\angle\)AOB and \(\angle\)AOC are supplementary angles, as the sum of these two angles is 120 + 60 = \(180^\circ\).
The methodology to find supplementary and complementary angles
For complementary angles
Let us find the complementary angle for an angle, say x. To find its complementary angle, subtract x from 90. So, the complementary angle for x is (90 – x) degrees.
For supplementary angles
Similarly, let us assume an angle y. To find its supplementary angle, subtract y from 180. So, the supplementary angle for y is (180 – y) degrees.
Some key points
1. The sum of supplementary angles is 180 degrees, so when we place them adjacent to each other, they form a straight angle.
2. Complementary and supplementary angles are always in pairs. So, three angles can never be supplementary, even though the sum of their angles is 180 degrees or 90 degrees.
3. The sum of two complementary angles is 90 degrees. Therefore, they form a right angle.
Rapid recall
Solved Examples: Complementary Angles and Supplementary Angles
Example 1: Find the complementary angle of 55 degrees.
Solution:
The sum of complementary angles is 90 degrees.
Therefore, the complementary angle of 55 degrees can be found as:
= 90°– 55°
= 35°
Hence, the complementary angle of 55 degrees is 35 degrees.
Example 2: Find the supplementary angle of 90 degrees.
Solution:
The sum of supplementary angles is 180 degrees.
Therefore, the supplementary angle of 90 degrees will be
= 180°– 90°
= 90°
Hence, the supplementary angle of 180 degrees is 90 degrees.
Example 3: Find ∠HFG in the following figure.
Solution:
∠EFH = 66 degrees
Here, ∠HFG and ∠EFH are complementary angles.
The sum of complementary angles is 90 degrees.
Therefore,
∠EFH = 90°– 66°
= 24°
Hence, the complementary angle of 66 degrees is 24 degrees.
A pair of angles that sum up to 180 degrees are known as supplementary angles. In other words, supplementary angles are those whose sum is always 180 degrees.
Complementary angles are those whose sum is always 90 degrees.
The sum of complementary angles is 90 degrees.
The sum of supplementary angles is 180 degrees.
90°, 40°, and 50° are not supplementary angles because supplementary angles are always in pairs.