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 }

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