Geometry
Vertically Opposite Angles – Equal Angles from Crossing Lines
When two straight lines cross, they form four angles at the intersection. The two angles that sit directly across from each other (not next to each other) are called vertically opposite angles, and they are always equal. Meanwhile, any two angles that sit right next to each other at that same crossing point form a straight line, so they're supplementary (sum to 180°) – combining everything you've learned in this section so far.
The name comes from the shared vertex (the crossing point) – “vertically” here refers to sharing that vertex, not to being physically up-and-down. Two intersecting lines always create exactly two pairs of vertically opposite angles.
Why Vertically Opposite Angles Are Equal
At a crossing point, adjacent angles are supplementary (sum to 180°), and this fact forces the opposite angles to be equal. Two crossing lines always create two pairs of equal vertically opposite angles.
The vertically opposite angle is equal: 65°. The two adjacent angles are supplementary: 180 − 65 = 115° each.
Real-Life Application
- Scissors: the two pairs of angles formed where the blades cross are vertically opposite.
- Road crossings: the angles at an X-shaped intersection come in vertically opposite pairs.
- Fabric patterns: criss-crossed weave patterns rely on equal vertically opposite angles.
Key Takeaways
- Vertically opposite angles are formed when two lines cross, and are always equal.
- Adjacent angles at the same crossing point are supplementary.
- Two crossing lines create two pairs of vertically opposite angles.