Understanding Angles and Supplements
In geometry, angles can be classified into various types, one of which is the "supplementary angle." Two angles are considered supplementary if the sum of their measures equals 180 degrees. To find an angle that is equal to its supplement, we need to set up an equation.
Setting Up the Equation
- Let the angle be represented as "x."
- Its supplement can then be described as "180 - x."
- According to the problem, these two angles are equal:
x = 180 - x
Solving the Equation
- To solve for x, we add x to both sides of the equation:
x + x = 180
- This simplifies to:
2x = 180
- Next, divide both sides by 2:
x = 90
The Angle
Thus, the angle that is equal to its supplement is:
- 90 degrees
Understanding the Result
- At 90 degrees, the angle perfectly bisects the 180-degree line.
- Its supplement (also 90 degrees) indicates that both angles are complementary, meaning they add up to 180 degrees.
Conclusion
In summary, the only angle that is equal to its supplement is:
- 90 degrees
This unique property makes 90 degrees a significant angle in geometry, often referred to as a right angle.