Vertically opposite angles
When two straight lines cross, they form pairs of vertically opposite angles. These are the angles directly opposite each other at the intersection, and they are always equal.
How to solve
- Locate the crossing lines. Find the intersection point and identify the angle you know.
- Find the opposite angle. The angle directly across from it has the same measure.
- Use equality. If one vertically opposite angle is given as an expression, set the opposite angle equal to it and solve for the unknown.
- Simplify the final answer. Combine like terms or reduce the expression if needed.
Check your work
- Make sure you chose the angle directly opposite, not an adjacent angle.
- If you solved for a variable, substitute it back to confirm both opposite angles match.
Key idea
Vertically opposite angles are equal, so the main task is usually to match the correct pair and simplify the resulting expression or number.