Supplementary Angles
Supplementary angles refer to the pair of angles that always sum up to 180°. These two angles are called supplements of each other. The word "supplementary" comes from two Latin words "Supplere" and "Plere" where "Supplere" means "supply”, whereas "Plere" means "fill". So, "supplementary" means "something when supplied to complete a thing".
In this lesson, we will explore the world of supplementary angles, which helps in solving various geometry problems. The journey will take us through supplementary angles, and the difference between complementary angles and supplementary angles.
What are Supplementary Angles?
Two angles are said to be supplementary angles if they add up to 180 degrees. Supplementary angles form a straight angle (180 degrees) when they are put together. In other words, angle 1 and angle 2 are supplementary, if Angle 1 + Angle 2 = 180°. In this case, Angle 1 and Angle 2 are called "supplements" of each other.
Observe the following figure in which 130° + 50° = 180°. Hence, by the definition of supplementary angles, these two angles are supplementary.
Adjacent and Non-Adjacent Supplementary Angles
Supplementary angles can either be adjacent or non-adjacent. So, there are two types of supplementary angles. Each of these types of supplementary angles is explained below.
- Adjacent supplementary angles
- Non-adjacent supplementary angles
Adjacent Supplementary Angles
Two supplementary angles with a common vertex and a common arm are said to be adjacent supplementary angles.
Example:
Here, ∠COB and ∠AOB are adjacent angles as they have a common vertex, O, and a common arm OB. They also add up to 180 degrees, that is, ∠COB + ∠ AOB = 70° + 110° = 180°. Hence, these two angles are adjacent supplementary angles.
Non-adjacent Supplementary Angles
Two supplementary angles that are NOT adjacent are said to be non-adjacent supplementary angles.
Example:
Here, ∠ABC and ∠PQR are non-adjacent angles as they neither have a common vertex nor a common arm. They also add up to 180 degrees, that is, ∠ABC+ ∠PQR = 79° + 101° = 180°. Hence, these two angles are non-adjacent supplementary angles. Non-adjacent supplementary angles, when put together, form a straight angle.
Complementary and Supplementary Angles
Supplementary and complementary angles are those angles that exist in pairs. While supplementary angles add up to 180°, complementary angles add up to 90°. These angles have numerous real-time applications, the most common being the crossroads. The following table shows the difference between supplementary and complementary angles.
The supplementary vs complementary angles table.
|
Complementary Angles |
Supplementary Angles |
|---|---|
|
Two angles are said to be complementary if they add up to 90 degrees. |
Two angles are said to be supplementary if they add up to 180 degrees. |
|
Complement of an angle x is (90 - x)° |
Supplement of an angle x is (180 - x)° |
Tips on Supplementary angles vs Complementary angles
Here is a short trick for you to understand the difference between supplementary angles and complementary angles.
- "S" is for "Supplementary" and "S" is for "Straight." Hence, you can remember that two "Supplementary" angles when put together form a "Straight" angle.
- "C" is for "Complementary" and "C" is for "Corner." Hence, you can remember that two "Complementary" angles when put together form a "Corner (right)" angle.
How to find the Supplement of an Angle?
When the sum of two angles is equal to 180°, then we call that pair of angles, supplements of each other. So, we know that the sum of two supplementary angles is 180 degrees, and each of them is said to be a "supplement" of the other. Thus, the supplement of an angle is found by subtracting it from 180 degrees. This means the supplement of x° is (180 - x)°
For example, the supplement of 77° is obtained by subtracting it from 180°. Thus, its supplement is (180-77)° = 103°.
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Supplementary Angles Examples
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Example 1:
Find angle Y in the following figure.
Solution
In the given figure, Y and 77° are supplementary angles as they lie at a point on a straight line. Hence, their sum is 180°.
Y + 77° = 180°
Y = 180° - 77° = 103°
Therefore, Y = 103°
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Example 3:
Find the value of x if the following two angles are supplementary.
Solution:
Since the given angles are supplementary, their sum is 180°.
x/2 + x/3 =180°
5x/6 =180°
x =180° × 6/5 = 216°
Therefore, the value of x is 216°. This means one angle is 216/2 = 108° and the other angle is 216/3 = 72°.
FAQs on Supplementary Angles
What are Supplementary Angles in Geometry?
In geometry, two angles are said to be supplementary angles if they add up to 180 degrees. For example, if ∠A + ∠B = 180°, then ∠A and ∠B are called supplementary angles. Supplementary angles always form a straight angle (180 degrees) when they are put together.
Can Two Acute Angles be Supplementary Angles?
No, if two angles are supplementary, then they are both either right angles or one of them is acute and one of them is obtuse. If two acute angles are put together, their sum will always be less than 180°, so two acute angles can never be supplementary angles.
Can Two Obtuse Angles be Supplementary Angles?
No, if two angles are supplementary, then they are both either right angles or one of them is acute and one of them is obtuse. If two obtuse angles are put together, their sum will always be greater than 180°, so two obtuse angles can never be supplementary angles.
Can Two Right angles be Supplementary Angles?
Yes, two right angles are always supplementary because 90° + 90° = 180°.
Are Supplementary and Complementary Angles the Same?
No, supplementary and complementary angles are not the same. Two angles form a pair of complementary angles when their sum is 90°, whereas, two angles form a pair of supplementary angles when their sum is 180°.
Can Three Angles be Supplementary?
No, three angles can never be supplementary even though their sum is 180 degrees. Though the sum of angles, 40°, 90° and 50° is 180°, they are not supplementary angles because supplementary angles always occur in pairs. The definition of supplementary angles holds true only for two angles.
What Angle is Supplementary to 84 Degrees?
The supplement of an angle is obtained by subtracting it from 180 degrees. Thus, the angle that is supplementary to 84 degrees is 180° - 84° = 96°.
What Angle is Formed if we Put the Supplementary Angles Together?
When a pair of supplementary angles are put together, they form a straight angle.
Complementary angles form what Type of Angle?
Two angles form a pair of complementary angles when their sum is 90°. So, the pair of complementary angles form a right angle.
What are Adjacent Supplementary Angles?
Adjacent supplementary angles are those angles that share a common arm and vertex and they always sum up to 180°.
What is the Sum of Two Supplementary Angles?
The sum of two supplementary angles is always 180°. Supplementary angles may be adjacent angles or non-adjacent angles but they always add up to 180°.
How to Identify Supplementary Angles?
Supplementary angles can be easily identified by their sum. If any two angles add up to 180°.