Supplementary Angles by Vedantu
Are you a lover of mathematics? And, your answer is in affirmative. So, if you are a fan of geometry, then Vedantu has brought something special for you. The mathematics experts at Vedantu have prepared the topic of supplementary angles for you. Here, you can explore the entire concept in one go. You will get to know about the definition, get to know about the different types of supplementary angles, their uses, the method of resolving them, associated formulas and much more. Are you feeling super excited, aren’t you? Well, you truly are as your learning sessions with Vedantu are going to be real fun with learning and revising regularly. Maintaining your enthusiasm, here you can start it by understanding the basic definition of supplementary angle and once you are versed with you can move ahead next.
What is a Supplementary Angle?
When the sum of the measure of two angles is 1800, then the pair of angles is said to be supplementary angles. We have studied basic geometrical terms. We know that two lines having a common vertex form an angle. Various parts of an angle are vertex, arms, interior, and exterior of angles. When two lines intersect they form four angles at the point of intersection. An angle is denoted by the symbol ∠.
From the figure, ∠ABC is an angle. B is the point of intersection called the vertex and AB and BC are the sides of the angle. Angles are commonly measured in terms of degree.
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Angles are classified according to their sizes as follows
Acute angle
Obtuse angle
Right angle
Reflex angle
Acute angle is an angle that is measured lesser than 90 degree while right angle is measured properly 90 degree. Obtuse angle is measured more than 90 degree and it is lesser than 180 degree. Reflex angle is an angle that is measured greater than the 180 degree but it is lesser than the 360 degree.
Vedantu tutors assert on the fact of practicing these as much as a student can. The reason behind this is that mathematics is a subject of regular practice and the more you practice the more your confidence level will be. So, sketch out a routine practice and stick to it on a daily basis. If you want to know more about these angles, then you are going to enhance your learning in the coming paragraphs. Keep scrolling and keep learning.
There are more types of angles on the basis of the pairs of angles. They are as follows
Complementary angles
Supplementary angles
Adjacent angles
Vertically opposite angles
Linear Pairs
In this session, we will be learning what is a supplementary angle?
Supplementary meaning is to complete or supply what is needed.
Understanding Supplementary Angles
We know that when the sum of the measure of two angles is 1800, then the pair of angles is said to be supplementary angles. Here the supplementary meaning is one angle is supplemented to another angle to make a sum of 1800.
From the figure, we can say that ∠1 + ∠2 = 1800
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But it is not necessary that the two supplementary angles are always adjacent to each other. They can be different angles, only their sum should be 1800.
From the figure, ∠3 and ∠4 are not adjacent but they make a supplementary angle if their sum is 1800.
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Properties of Supplementary Angles
Two angles are said to be a supplementary angle if the sum of their measures is 1800.
It is not necessary that a supplementary angle will lie on the same line, they can be on different lines but should measure 1800.
In the supplementary angles if one is an acute angle then the other is an obtuse angle.
In supplementary angles, if one angle is 900 then the other angle will also be 900.
Above mentioned are the different properties where an angle is known as supplementary. Hence, students have to start revising the concept in mind. Always remember that it is not the score that is your target but it should always be the basic clarity of concept. The reason behind it is that you can never score well if the clarity of concept is not strong in your mind. And, maths is a subject that is pillared on concepts, formulas, and equations.
Supplementary Theorem
If a ray stands on a line, then the sum of two adjacent angles so formed is 1800.
If two angles let ∠A and ∠B are both supplementary to a third angle be ∠C, then ∠A and ∠B are congruent.
If ∠A + ∠C = 1800
∠B + ∠C = 1800 then ∠A = ∠B.
How to Find two Angles are Supplementary?
If the measure of two angles are given. Add them. If the sum of the measure of these two angles is 1800, then the two angles are supplementary angles.
If the two angles are given as supplementary angles and if the measure of one angle is given we can find the other angle.
For example: ∠A + ∠B = 1800 and ∠A = 800 , then ∠B = ?
∠B = 180 - ∠A
∠B = 180 - 80
∠B = 1000
Adjacent and Non-Adjacent Supplementary Angles
Supplementary Angles can be classified as adjacent supplementary angles and non- adjacent supplementary angles.
Supplementary angles that share one common arm are called adjacent supplementary angles.
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Adjacent supplementary angles
Supplementary angles that do not share any common arm and are totally two different angles then they are called non-adjacent supplementary angles.
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Non-adjacent supplementary angles
Solved Examples
Example 1: Two angles are supplementary. One of these two angles is 500 find the other angle.
Solution :
Let the other angle be x
Given that the two angles are supplementary we have,
The sum of the measures of these two angles is 1800
x + 50 = 1800
x = 180 - 50
x = 1300
So the other angle is 1300
Example 2: Two angles are supplementary and one of them is 71°. What is the size of the other angle?
Solution: Let ‘a’ be the size of the other angle.
Given that the two angles are supplementary.
Then by supplementary angles definition, we have
The sum of the measures of these two angles is 1800
a + 71 = 180
a = 180 - 71
a = 1090
Therefore the size of the other angle is 1090.
Quiz Time
Two angles are supplementary and one of them is twice as big as the other. What is the size of the smaller angle?
Two angles are supplementary and one of them is 1370. What is the size of the other angle?
Vedantu has deliberately not resolved these two questions. It is for the students to practice and find the right answer themselves. If they are encountering any sort of challenges, they can connect to the Vedantu experts. For studying mathematics, Vedantu also advises you to form a group where you can share your thoughts and doubts that the collective study will bring better results for them. After all, different minds bring different ways of understanding the concept.
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FAQs on Supplementary Angles
1. What is the Difference Between Supplementary Angles and Complementary Angles?
If the sum of the measure of two angles is 1800 then the angles are said to be supplementary angles, whereas if the sum of measures of two angles is 900 then the angles are called complementary angles.
Supplementary angles together form a straight line whereas complementary angles together form a right angle.
Two angles ∠A and ∠B are supplementary angles if ∠A + ∠B =1800, while two angles ∠A and ∠B are complementary if ∠A + ∠B = 900
Example of supplementary angle
∠1 + ∠2 = 1800
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Example of Complementary angle
∠1 + ∠2 = 900
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2. Can two Obtuse Angles be Supplementary?
No two obtuse angles cannot be supplementary because according to the definition of obtuse angle an angle is called an obtuse angle if its measure is greater than 900. And if two obtuse angles are added their measure will be more than 1800 which contradicts the definition of the supplementary angle. Two angles are supplementary if the sum of the measures of their ankle is1800.
For example, consider two obtuse angles of measures 1000 and 1100 then the sum will be 1000+ 1100 = 2100
Hence the result of the sum of two obtuse angles is 2100 which is greater than the supplementary angles.
So we can say that two obtuse angles cannot be supplementary.
3. Can Two Acute Angles be Supplementary?
No, two acute angles cannot be supplementary angles because according to the definition of acute angle an angle is called an acute angle if its measure is less than900. And if two acute angles are added then their sum will be less than 1800 which contradicts the definition of the supplementary angle. The sum of the measures of the supplementary angle is 1800. So, this way, you will be able to find the fact whether two acute angles can be supplementary or not.