Intersecting lines
When two straight lines cross, they meet at one point and make four angles. These four angles are linked by two simple rules.
Vertically opposite angles
Key idea
Vertically opposite angles are equal. They are the pair of angles that face each other across the crossing point.
If two lines cross and one angle is 70°, the angle directly opposite it is also 70°.
Adjacent angles on a straight line
Two angles that sit next to each other along one of the straight lines are adjacent angles on a line, and they add up to 180°. Because of this, the four angles around the crossing come in two equal pairs.
So if one angle is ∠a, then:
- the angle opposite it = ∠a,
- each angle next to it = 180° − ∠a.
Worked example
Two lines cross. One of the four angles is 125°. Find the other three angles.
The angle vertically opposite the 125° angle = 125°.
An adjacent angle on the line = 180° − 125° = 55°.
The angle opposite that one = 55°.
Check: 125° + 55° + 125° + 55° = 360°, a full turn. Correct.
Remember
- Vertically opposite angles are always equal.
- Angles side by side on a line add to 180°.
- The four angles at a crossing add up to 360°.