Supplementary angles
Supplementary angles are two angles whose measures add up to 180 degrees. In Grade 6 Saxon Math Course 1, students use the supplementary relationship to find a missing angle: if one angle measures 65°, its supplement is 180° − 65° = 115°. Supplementary angle pairs commonly arise when a straight line is intersected by another line, forming two angles on one side that together span 180°. This relationship is used throughout geometry proofs and calculations involving parallel lines and transversals.
Key Concepts
Property Supplementary angles are two angles whose measures total $180^\circ$.
Examples An angle of $120^\circ$ and an angle of $60^\circ$ are supplementary because $120^\circ + 60^\circ = 180^\circ$. The supplement of a $90^\circ$ angle is another $90^\circ$ angle, since $180^\circ 90^\circ = 90^\circ$. If $\angle X$ and $\angle Y$ are supplementary and $\angle X = 45^\circ$, then $\angle Y = 135^\circ$.
Explanation Picture a perfectly straight line, which forms a $180^\circ$ angle. If you draw a ray from any point on that line, you create two new angles. These two angles are 'supplementary' because they team up to perfectly form the complete straight line. They are the ultimate partners in flatness!
Common Questions
What are supplementary angles?
Two angles whose measures sum to 180°.
If one angle measures 65°, what is its supplement?
180° − 65° = 115°.
Are supplementary angles always adjacent (next to each other)?
No. Two angles are supplementary based solely on their sum equaling 180°, regardless of their position.
What angle is its own supplement?
90°. A right angle is its own supplement: 90° + 90° = 180°.
How are supplementary angles formed by a straight line?
When a ray meets a straight line, the two angles formed on one side of the line are supplementary because together they make a straight angle of 180°.