Two angles are said to be supplementary when the sum of their measures equals 180 degrees. If we have two angles, let’s call them A and B, both of which are supplementary to the same angle C, we can derive an important conclusion.
In this case, since both angle A and angle B satisfy the condition of adding up to 180 degrees with angle C, we can set up the following equations:
- A + C = 180 degrees
- B + C = 180 degrees
To find the relationship between angles A and B, we can manipulate these equations:
From the first equation, we can express angle A:
- A = 180 degrees – C
From the second equation, we can express angle B:
- B = 180 degrees – C
Since both expressions for angles A and B are equal (as they both equal 180 degrees – C), we can conclude that:
- A = B
This means that if two angles are supplementary to the same angle, then those two angles are equal to each other. This property is a direct result of the definition of supplementary angles and can be a useful concept in geometry.