Find the adjacent angle on a straight line
Supplementary angles total 180°. They commonly form a linear pair where a ray divides a straight line, but they can be separate angles if the problem states their sum. The unknown value is 180° minus the known angle.
For a known angle θ between 0° and 180°, its supplement is 180°−θ. This is different from the reflex angle around the outside, which is 360°−θ, and from a complement, which completes a right angle.
Solve a linear-pair problem
- Check for opposite rays forming a straight line, or for a statement that the two values are supplementary.
- Enter the known interior angle from 0° to 180°.
- Add the calculated value to the original and verify a 180° total.
- At an intersection, identify whether the requested angle is adjacent (supplementary) or vertical (equal to the original).
Worked straight-line examples
- An angle of 128° beside a straight line has a 52° supplement.
- If one angle at an intersection is 71°, each adjacent angle is 109°, while the opposite vertical angle is 71°.
- The supplement of 0° is 180°, and the supplement of 180° is 0°.
- A 92.4° measured interior angle has an 87.6° adjacent supplement.
- Three angles on one side of a straight line may also sum to 180°; subtract both known parts to find the third.
Where 180-degree sums appear
- Linear pairs at intersecting streets or diagram lines.
- Same-side angle relationships in parallel-line exercises.
- A known interior angle and its adjacent exterior angle.
- Checking several sectors arranged along a straight baseline.
Do not infer a linear pair from proximity
Two angles drawn beside each other are supplementary only when their outer sides form a straight line or another given condition establishes a 180° sum. Perspective and imprecise sketches can make a line look straight when it is not.