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 / 要点
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 / 例题
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 / 记住
- 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°.