Naming angles
Before the rules, a quick vocabulary check, because giving a reason for each step is part of the marks.
| Name | Size |
|---|---|
| Acute | less than \(90^\circ\) |
| Right | exactly \(90^\circ\) |
| Obtuse | between \(90^\circ\) and \(180^\circ\) |
| Reflex | between \(180^\circ\) and \(360^\circ\) |
A full turn is \(360^\circ\) and a half turn is \(180^\circ\). Those two facts are behind everything below.
Angles on a straight line
Angles that sit together along a straight line make a half turn, so they add up to \(180^\circ\).
Three angles meet on a straight line. They measure \(47^\circ\), \(x\), and \(68^\circ\). Find \(x\).
Add the knowns first
Total up every angle you already have, then take that from \(180^\circ\) (or \(360^\circ\)). Doing the addition before the subtraction keeps the arithmetic clean.
Angles around a point
When several angles meet at a single point and fill the space all the way round, they make a full turn, so they add up to \(360^\circ\).
Four angles meet at a point: \(90^\circ\), \(145^\circ\), \(60^\circ\) and \(y\). Find \(y\).
Vertically opposite angles
When two straight lines cross, they make four angles. The two angles that sit opposite each other, tip to tip, are equal. These are vertically opposite angles.
- Vertically opposite angles
- The pair of angles facing each other where two lines cross. They are always equal. The other pair is equal too, and each neighbouring pair adds to \(180^\circ\) because they sit on a straight line.
So if two lines cross and one angle is \(110^\circ\), the angle directly opposite it is also \(110^\circ\), while each angle next to it is \(180 - 110 = 70^\circ\).
Where this is assessed
Choosing the right rule and computing the angle is Criterion A (Knowing and understanding). Writing the reason next to each line, such as "angles on a straight line = 180", is Criterion C (Communicating), and it is often worth its own mark.
Check yourself
1. Two angles sit together on a straight line. One is \(118^\circ\). Find the other. +
Angles on a straight line add to \(180^\circ\), so the other is \(180 - 118 = \mathbf{62^\circ}\).
2. Three angles meet at a point: \(90^\circ\), \(145^\circ\) and \(x\). Find \(x\). +
Angles around a point add to \(360^\circ\): \(x = 360 - 90 - 145 = \mathbf{125^\circ}\).
3. Two straight lines cross. One of the angles formed is \(55^\circ\). State the vertically opposite angle and one angle next to it. +
The vertically opposite angle equals it, so it is \(\mathbf{55^\circ}\). An angle next to it sits on a straight line with it, so it is \(180 - 55 = \mathbf{125^\circ}\).
Part of the Standard Maths library. Spotted an error or want a topic added? That feedback makes the notes better.