Understanding Complementary Angles in Geometry

There are various types of angles we come across in geometry. One of them is complementary angles. It is a basic concept one must know while studying geometry. The math program at 98thPercentile teaches about all this and much more. Join our 1-week free trial classes now and enhance your child’s knowledge by helping them understand concepts.  

Complementary angles are one of the fundamental ideas you will encounter when studying geometry. They can be thought of as angles that combine to form a right angle or 90 degrees. Two angles are complementary if their measurements total up to 90 degrees. For instance, two angles must be equal if one is 30 degrees and the other is 60 degrees. They form the ideal 90-degree straight angle when combined! 

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What are Complementary Angles? 

Two angles that sum up to 90 degrees are said to be complementary. Like parts of a puzzle, they "complete" one another to form a right angle. To make 90 degrees, for instance, if one angle is 40 degrees, the second angle in the pair would be 50 degrees. 

What are the Types of Angles? 

Less than 90 degrees is known as the acute angle. 
If an angle is 90 degrees exactly, it is a right angle. 
An obtuse angle is one that is greater than 90 degrees but less than 180. 
Exactly 180 degrees is a straight angle. 
More than 180 but less than 360 degrees is the reflex angle. 

What are the Types of Complementary Angles? 

There are 2 types of complementary angles 

• Two angles that are adjacent to one another and have a common side are said to be adjacent complementary angles. 

• Two angles that add up to 90 degrees but do not share a side or a common point are known as non-adjacent complementary angles. 

Examples of Complementary Angles 

Two angles that add up to precisely 90 degrees are said to be complementary. To create a right angle, they complete one another. For instance

• The complement of a 30-degree angle is 60 degrees.  

• In order to reach 90 degrees, there must be two 45 degrees. 

When combined, these pairs of angles will always equal 90 degrees, regardless of whether they are adjacent or non-adjacent. 

Finding Complementary Angles 

Subtract the specified angle from 90 degrees to find a complementary angle. For instance, the complement of a 30-degree angle is 60 degrees, which is obtained by subtracting 30 from 90 degrees. The sum of these two angles is 90 degrees or a straight angle. 

Complementary Angles' Attributes  

• 90 degrees is always the sum of complementary angles.  
  

• They may be non-adjacent or neighboring (next to one another).  
  

• The formation of a right angle occurs when neighboring complementary angles form a right angle. 

How Do Complementary Angles Help? 

There are many mathematical and practical uses for complementary angles. To guarantee structural accuracy, architects, for example, utilize them when creating rooms or halls with right angles. They assist us in determining unknown angles in geometry problems, which is useful when constructing precise models or solving larger shapes. 

In a nutshell, two angles that add up to 90 degrees are complementary. Gaining the ability to recognize and manipulate them will help you develop strong geometrical abilities that you may use in everything from simple algebra to practical design. Join 98thPercentile to know more. 

FAQs (Frequently Asked Questions) 

Q.1 What do complementary angles mean? 

Ans: If two angles sum up to 90 degrees, they are considered complementary angles in geometry.  

Q.2: What is a complementary angle pair? 

Ans: When two angles add up to 90°, they constitute a pair of complementary angles. Thus, a right angle is formed by the complementary angles. 

Q.3: How can complementary angles be found? 

Ans: Two angles are considered complementary if their sum equals 90 degrees. Therefore, subtracting an angle from 90 yields its complement. For instance, 90° - 40° = 50° is the complement of 40°. 

Q.4: Are two right angles complementary? 

Ans: A right angle measures 90°. Two straight angles added together will equal 180°, which is more than 90°. Therefore, two right angles are never complimentary. 

Q.5: How do complementary and supplementary angles differ from one another? 

Ans: While the sum of two complementary angles is 90 degrees, the supplementary angles are those whose sum is 180 degrees. Two complementary angles form a right angle, and two supplementary angles form a straight angle.

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