Hi there. In this mathematics post, I would like to cover complementary and supplementary angles. This topic is not particularly difficult but complementary and supplementary angles do get mixed up sometimes.

If you are wondering about applications for this. I cannot think of one. This topic just helps with understanding some math jargon. 

<center><img src="https://cdn.pixabay.com/photo/2013/07/13/13/36/triangle-161210_960_720.png" /></center>
<center><a href="https://cdn.pixabay.com/photo/2013/07/13/13/36/triangle-161210_960_720.png">Pixabay Image Source</a></center>


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## Topics
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* What Are Complementary and Supplementary Angles?
* A Memory Aid
* Checking If Two Angles Are Complementary or Supplementary
* Solving For Missing Angles With Examples

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## What Are Complementary and Supplementary Angles?
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Two angles measurements are considered **complementary** if these two angles add up to **90 degrees**.

When two angles add up to **180 degrees** the two angles are supplementary angles.


<center>![complementary-supplementary-angles.png](https://images.hive.blog/DQmRjL7m1UraNggbYbtVmQ61L5DyxU5oBRQZiFF7uvH8WMD/complementary-supplementary-angles.png)</center>

<center>Picture From [onlinemathlearning.com](https://www.onlinemathlearning.com/complementary-angles.html)</center>


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## A Memory Aid
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From time to time, we do forget stuff that we have learned from the past. I am no different. Recently, I have developed a useful memory aid for remembering complementary and supplementary angles.

The first letter from complementary is `c` which is before `s` from supplementary. The letter `c` being before `s` relates with 90 degrees being less than 180 degrees.

<center>`complementary angles ---> 90`</center>

<center>`supplementary angles ---> 180`</center>

<center><img src="https://cdn.pixabay.com/photo/2018/04/20/20/59/mental-health-3337026_960_720.jpg" /></center>
<center><a href="https://cdn.pixabay.com/photo/2018/04/20/20/59/mental-health-3337026_960_720.jpg">Pixabay Image Source</a></center>


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## Checking If Two Angles Are Complementary or Supplementary
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It is actually easy to check if two angles are complementary or supplementary. The hardest part might be remembering if complementary angles go with 90 degrees or 180 degrees. If two angles add up to 90 degrees then those two angles are complementary angles. If the two angles add up to 180 degrees then the two angles are supplementary. You can also have the case where the two angles are neither supplementary nor complementary angles.

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| Angle 1 + Angle 2  | Conclusion Of Two Angles  |
|---|---|
| 90 degrees  | Complementary  |  
| 180 degrees  | Supplementary  |  
| Not 90 degrees nor 180 degrees   | Neither  | 

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## Solving For Missing Angles With Examples
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Algebra tools and skills can be used to solve for missing angles. Here are some examples:

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**Example One**

What is the complement of a 30 degree angle?

Finding the complement of a 30 degree angle involves finding a second angle `x` such that `30 + x = 90`. The complement of the 30 degree angle would be 60.

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**Example Two**

Determine the supplement of a 110 degree angle.

Two angles are supplementary when the sum of the two angles equal 180 degrees. The supplement of the 110 degree angle would be 70 degrees as `110 + 70 = 180`.

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**Example Three**

A right angle is bisected into two equal angles. What are the two equal angles?

Knowing that a right angle is 90 degrees, you can take half of 90 to obtain 45. The two equal angles are 45 degrees and 45 degrees.

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**Example Four - Algebraic**

An acute angle of `x` degrees is supplementary to an obtuse angle named `y`. What is the measure of this obtuse angle?

As the two angles are supplementary we can start with this equation:

<center>`x + y = 180`</center>

Subtracting both sides by `x` gives the measure of the obtuse angle `y`.

<center>`y = 180 - x`</center>

This particular example is a bit theoretical and abstract. Given an acute angle such as 70 degrees, the second angle can be computed by doing 180 minus the given 70 degrees. The obtuse angle in this case would be 110 degrees.

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**Example Five - Solve For `x` & Angles**

There are two angles that are complementary to each other. The first angle is `x + 20` and the second angle is `x + 10`. What is the value of `x` and what are the two angle measures?

As the two angles are complementary, the sum of the two angles equal to 180 degrees. We can set up this equation and solve for `x`. 

<center>https://quicklatex.com/cache3/5d/ql_2d41bdbb780ffc61258167b40fa6fb5d_l3.png</center>

This makes the two angles 50 degrees and 40 degrees after substituting the value of 30 degrees for `x`.

<center><img src="https://cdn.pixabay.com/photo/2015/11/05/08/21/geometry-1023846_960_720.jpg" /></center>
<center><a href="https://cdn.pixabay.com/photo/2015/11/05/08/21/geometry-1023846_960_720.jpg">Pixabay Image Source</a></center>

<center>Thank you for reading.</center>

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