Supplementary Angles
Supplementary angles are two angles whose sum is 180° (π radians).
In simpler terms, two angles are "supplementary" if their sum equals a straight angle.
This is true regardless of the angles' position or orientation.
The concept of supplementary angles applies only to pairs of angles. Thus, a single angle cannot be supplementary; it takes two.
A Practical Example
Consider the following two angles:
$$ \alpha = 60° $$
$$ \beta = 120° $$
These angles are supplementary because their measures add up to 180°.
$$ \alpha + \beta = 180° $$
The result of this addition is a straight angle.
Key Points
Supplementary angles have several interesting properties:
- Every angle has a supplementary angle
Given any angle, you can find its supplementary angle by subtracting its measure from 180 degrees. For example, if angle alpha measures 120° $$ \alpha = 120° $$ then its supplementary angle beta is 60° $$ \beta = 180° - \alpha = 180° - 120° = 60° $$ Thus, for any given angle, you can always determine its supplementary angle by calculating the difference.
- When two lines intersect, consecutive angles taken in pairs are supplementary
This property is frequently used in solving geometric problems and proving theorems.
- Adjacent angles are always supplementary (and vice versa)
Two angles are considered "adjacent" if they share a common side and the non-common sides are extensions of the same line. Therefore, to find the supplementary angle of a given angle, you just need to identify its adjacent angle.
And so forth.
