Supplementary and Complementary Angles
Here is a look at two of the relationships.
Supplementaryangles are two angles that have a sum of 180°.
Complementaryangles are two angles that have a sum of 90°.
There is an easy way to try and remember these using the first letters of each word.
The Sin supplementarycan be used to form the 8 in 180.
The Cin complementarycan be used to form the 9 in 90.
If we know that a set of angles form one of these special relationships, we can determine the measure of the other angle.
Example #1: 43°
To determine the supplement, subtract the given angle from 180.
180 - 43 = 137° The supplement of 43° is 137°.
To determine the complement, subtract the given angle from 90.
90 - 43 = 47° The complement of 43° is 47°.
Example #2: 61°
180 - 61 = 119° The supplement of 61° is 119°.
90 - 61 = 29° The complement of 61° is 29°.
Example #3: 127°
180 - 127 = 53° The supplement of 127° is 53°.
127° is already greater than 90°. Therefore, there is no complement.
Example #4: Determine the missing angle.
Notice that the two angles for a right angle when together. This means that the angles are complementary and have a sum of 90°.
90 - 62 = 28°
The missing angle measures 28 degrees.
Example #5: Determine the missing angle.
These two angles form a straight line. Straight lines measure 180°. That means that these two angles are supplementary.
180 - 77 = 103°
The missing angle measures 103 degrees.
Complementary angles form a right angle (L shape) and have a sum of 90 degrees.
Supplementary angles form a straight line and have a sum of 180 degrees.
If the relationship is given, you can subtract the given angle from the sum to determine the measure of the missing angle.
Two angles are Complementary when they
add up to 90 degrees (a Right Angle ).
These two angles (40° and 50°) are Complementary Angles, because they add up to 90°:
Notice that together they make a right angle.
But the angles don't have to be together.
These two are complementary because 27° + 63° = 90°
Play With It ...
(Drag the points)
Right Angled Triangle
In a right angled triangle, the two non-right angles are complementary, because in a triangle the three angles add to 180°, and 90° has already been taken by the right angle.
|When two angles add to 90°, we say they "Complement" each other. |
Complementary comes from Latin completum meaning "completed" ...
because the right angle is thought of as being a complete angle.
|Spelling: be careful, it is not"Complimentary Angle" (with an "i") ... |
that would be an angle you get for free!
Complementary vs Supplementary
A related idea is Supplementary Angles - those add up to 180°
How to remember which is which? Well, alphabetically they are:
- Complementary add to 90°
- Supplementary add to 180°
You can also think:
- "C" of Complementary is for "Corner" (a Right Angle), and
- "S" of Supplementary is for "Straight" (180° is a straight line)
Or you can think:
- when you are right you get a compliment (sounds like complement)
- "supplement" (like a vitamin supplement) is something extra, so is bigger
Supplementary AnglesSymbols in GeometryDegrees (Angle)Angles On a Straight LineAngles Around a PointParallel Lines and Pairs of AnglesInterior AnglesGeometry Index
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When the sum of the measures of two angles is 90°, such angles are called complementary angles and each angle is called a complement of the other.
The vertices of two angles may be same or different. In the given figure ∠AOB and ∠BOC are complementary as ∠AOB + ∠BOC = 30° + 60° = 90°.
Again, ∠PQR and ∠QRP are complementary as ∠PQR + ∠QRP = 40° + 50° = 90°.
Angles of measure 25° and 65° are complementary angles. The angle of 25° is the complement of the angle of 65° and the angle of 65° is the complement of the angle of 25°.
The complement of an angle of measure 32° is the angle of 58°. And, the complement of the angle of measure 58° is the angle of 32°.
(i) If two are complement of each other, then each is an acute angle. But any two acute angles need not be complementary.
For example, angles of measure 30° and 50° are not complement of each other.
(ii) Two obtuse angles cannot be complement of each other.
(iii) Two right angles cannot be complement of each other.
Worked-out Problems on Complementary Angles:
1. Find the complement of:
90° - 68°
Therefore, the complement of 68° is 22°
90° - 27°20'
= 89°60' - 27°20'
Therefore, the complement of 27°20' is 62°40'
(c) x + 52°
90° - (x + 52°)
= 90° - x + 52°
= 38° - x
Therefore, the complement of x + 52° is 38° - x
2. Find the complement of the angle (10 + y)°.
Complement of the angle (10 + y)° = 90° - (10 + y)°
= 90° - 10° - y°
= (80 - y)°
3. Find the measure of an angle which is 46° less than its complement.
Let the unknown angle be x, then measure of its complement = 90 - x
According to the question,
(90 - x) - x = 46°
90 - x - x = 46°
90 - 2x = 46°
90 - 90 - 2x = 46° - 90
-2x = 46° - 90
-2x = 46° - 90
-2x = -44°
2x = 44°
x = 44/2
x = 22°
Therefore, 90 - x (Put the value of x = 22°)
= 90 - 22°
Therefore, the pair of complementary angles are 68° and 22°
● Lines and Angles
Fundamental Geometrical Concepts
Classification of Angles
Some Geometric Terms and Results
Complementary and Supplementary Angles
Linear Pair of Angles
Vertically Opposite Angles
Parallel and Transversal Lines
7th Grade Math Problems
8th Grade Math Practice
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How do you find the supplement of 52 degrees?
What is the complement and the supplement of 52 degrees
- The complement is 38 degrees because you subtract 52 – 90 = 38.
- The supplement is 128 because you do 180-52=128.
- thank you so much.
- I meant 90-52.
What is the supplement of 62 degrees?
What is the complement of 27 degrees?
The complement of 27° is the angle that when added to 27° forms a right angle (90° ).
What is the supplement of an angle measuring 59 degrees?
The supplement is 121∘ .
What is the complementary angle of 28?
What is the measure of the complement of degree?
When two angles add to 90°, we say they “Complement” each other.
What is the measure of the complement of a 9 angle?
X=81 DEGREES. IS THE COMPLEMENT ANGLE.
What is the supplement of 57 degree angle?
What is the supplement of a 60 degree angle?
The supplementary angle of 60∘ is 120∘ .
What is the complement and supplement of 60 degrees?
Finally complement of the supplement of twice the angle 60°=90°-60°=30°.
What is the supplement of 63 degrees?
Trigonometry Examples The supplement of 63° is the angle that when added to 63° forms a straight angle (180° ).
What is the supplement of 58 degrees?
Trigonometry Examples The supplement of 58° is the angle that when added to 58° forms a straight angle (180° ).
Are the angles 63 degree and 27 degree complementary?
(ii) 63°+27°=90°63°+27°=90° These are complementary angles.
What is the complementary and supplementary angle of 63 degree?
supplementary to the complement = 180°-90° = 90° which is complement. (90–63)° = 27°.
Can two angles be supplementary if both of them are acute?
Thus, the two acute angles cannot be supplementary angles. Thus, the two obtuses angles cannot be supplementary angles.
What is the measure of an angle complementary to 70?
1. Complement of 70 is 90-70= 20 degrees.
2021-06-19Alex SmithMathSours: https://rehabilitationrobotics.net/how-do-you-find-the-supplement-of-52-degrees/
Degrees 27 complement of
Its a very simple one: The complement of an angle is what, when added to it, equals 90 degrees (90°). This means that the complement of 85° is 5°, since they add up to equal 90 degrees a right angle. The supplement of an angle is what, when added to it, equals 180 degrees. For example, in your problem, 180°-85°=95°.
Click to see full answer
Correspondingly, what is the complement of a 39 degree angle?
You are correct in setting up the equation, and your final answer is correct; you probably typoed when you wrote "180 = 219" when it should be "180 = 219 - x." And the complement of 39 degrees is 90 - 39 = 51 degrees.
Additionally, how do you find the complement and supplement of an angle? To determine the supplement, subtract the given angle from 180. 180 - 43 = 137° The supplement of 43° is 137°. To determine the complement, subtract the given angle from 90. 90 - 43 = 47° The complement of 43° is 47°.
In this manner, what is the complement of an angle?
Two Angles are Complementary when they add up to 90 degrees (a Right Angle). They don't have to be next to each other, just so long as the total is 90 degrees.
What is the supplement of the complement of 42 degree angle?
For you to get the complement of 42 degrees, subtract 42 degrees from 90 degrees. 48 degrees is the complement of 42 degrees.
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