# Complementary angles explained

Learn about complementary angles. I will explain what are complementary angles with examples. So first read the definition and see the examples for better understanding.

When we talk about complementary angles we should also talk about supplementary angles. These both angles we should know i.e. complementary angles and supplementary angles. The definitions of these both angles are almost same but there is a little difference. As of know we will learn complementary angles.

## Definition of complementary angles:

Any two angles we can call it as complementary angles when sum of those angles gives right angle i.e. ${ 90 }^{ 0 }$. The meaning of the definition is if we take any two angles and if we add them and if the sum is right angle then we can call them as complementary angles.

Examples:

${ 56 }^{ 0 }$ and ${ 34 }^{ 0 }$

${ 17 }^{ 0 }$ and ${ 73 }^{ 0 }$

${ 35 }^{ 0 }$ and ${ 55 }^{ 0 }$

In the above three pairs of examples, if we take any one pair and if we add we will get ${ 90 }^{ 0 }$ so they are complementary angles.

Let us take first pair i.e. ${ 56 }^{ 0 }$ and ${34 }^{ 0 }$.

Add the two angles i.e. ${ 56 }^{ 0 }$ + ${ 34 }^{ 0 }$ = ${ 90 }^{ 0 }$. We are getting the sum as ${ 90 }^{ 0 }$ so ${ 56 }^{ 0 }$ and ${ 34 }^{ 0 }$ are complementary angles.

Example problems:

The ratio of complementary angles is 5 : 13 then find the angles.

Solution:

Let the two angles be 5${ x }^{ 0 }$ and 13${ x }^{ 0 }$.

According to problem,

5${ x }^{ 0 }$ + 13${ x }^{ 0 }$ = ${ 90 }^{ 0 }$

18${ x }^{ 0 }$ = ${ 90 }^{ 0 }$

x = $\frac { 90 }{ 18 }$ = 5

Therefore the two angles are

5${ x }^{ 0 }$ = 5 x ${ 5 }^{ 0 }$ = ${ 25 }^{ 0 }$

13${ x }^{ 0 }$ = 13 x ${ 5 }^{ 0 }$ = ${ 65 }^{ 0 }$