Angles
Estimating angles
You can estimate the size of an angle in degrees by comparing it to a right angle. This helps you describe how far to turn.
Right angles and turns
One right angle is 90°. Counting in right angles: • two right angles = 180° (a straight line) • three right angles = 270° • four right angles = 360° (a full turn). After turning four right angles you face the same way you started.
Useful angles to remember
Some angles are helpful for estimating: • Half a right angle = 45° • A right angle = 90° • Halfway to a straight line = 135° • A straight line = 180°. Compare an angle to these to make a good estimate.
Using the decision tree
To estimate an angle, ask questions in order: 1. Is the angle greater than 90°? 2. Is it closer to 90° or to 0° (or to 180°)? This tells you which range the angle is in — 0–45°, 45–90°, 90–135° or 135–180° — then you make a closer estimate.
Worked examples
Counting right angles
- One right angle is 90°.
- Three right angles is 3 × 90°.
- 3 × 90 = 270.
Answer: Three right angles make 270°.
Estimating an acute angle
- The angle is less than 90°.
- It is closer to 90° than to 0°.
- So it is between 45° and 90° — about 65°.
Answer: A good estimate is about 65°.
Estimating an obtuse angle
- The angle is greater than 90°.
- It is closer to 90° than to 180°.
- So it is between 90° and 135° — about 110°.
Answer: A good estimate is about 110°.
Where you see this in real life
- Telling someone how far to turn to find a treasure chest in a game.
- Describing which way to walk using an angle.
- Estimating how far a door has been pushed open.
Key words
- Estimate
- A sensible guess of a size, close to the real answer.
- Right angle
- An angle of 90°, the angle of a quarter turn.
- Straight line
- An angle of 180°, made by two right angles.
- Full turn
- A turn of 360°, made by four right angles.