Find the angle which is equal to its supplement.

To find the angle that is equal to its supplement, we first need to understand what a supplement is. The supplement of an angle is what, when added to that angle, equals 180 degrees. So, if we denote the angle as \( x \), we can express its supplement as \( 180 - x \). The problem states that the angle is equal to its supplement, which gives us the equation:

Setting Up the Equation

We can write this relationship mathematically as:

x = 180 - x

Solving for x

To solve for \( x \), we can start by adding \( x \) to both sides of the equation:

x + x = 180

This simplifies to:

2x = 180

Finding the Value of x

Next, we divide both sides by 2 to isolate \( x \):

x = 90

Understanding the Result

The angle that is equal to its supplement is 90 degrees. This makes sense because the supplement of 90 degrees is also 90 degrees (since \( 180 - 90 = 90 \)).

Visualizing the Concept

To visualize this, think of a straight line that represents 180 degrees. If you place a 90-degree angle on one side, you will see that the remaining angle on the other side is also 90 degrees, confirming that both angles are equal.

Summary

In summary, the angle that is equal to its supplement is 90 degrees. This is a unique case in geometry, as it is the only angle that satisfies this condition. Understanding this concept can help you with more complex problems involving angles and their relationships.