Angles on a Straight Line – A Real-World Supplementary Pair
Whenever a ray splits a straight line into two angles, those two angles are always supplementary – they sum to exactly 180°, since together they make up the straight line itself. This is one of the most useful applications of the supplementary-angles rule you just learned, because it shows up constantly in diagrams: any time you see an angle sitting right next to a straight line, its “partner” angle is simply 180° minus itself.
This pair is sometimes also called a linear pair, since the two angles together form a single straight line.
The Straight-Line Rule
Angles that sit next to each other on a straight line always sum to 180°. If one angle is known, the other is 180° minus that angle.
x + 3x = 180. 4x = 180. x = 45°. The angles are 45° and 135°.
Real-Life Application
- Road forks: a road splitting into two directions from a straight road forms a linear pair of angles.
- Y-shaped supports: structural braces often split a straight beam into two measurable angles.
- Scissor cuts: cutting a straight strip at an angle creates two supplementary angles at the cut.
Key Takeaways
- Angles on a straight line (a linear pair) always sum to 180°.
- This is a real-world application of the supplementary-angles rule.
- Algebraic versions can be solved by setting the sum of the expressions equal to 180.
Practice: Angles on a Straight Line
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