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Estimating angles

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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.

Acute< 90°Right= 90°Obtuse90°–180°Reflex> 180°

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

  1. One right angle is 90°.
  2. Three right angles is 3 × 90°.
  3. 3 × 90 = 270.

Answer: Three right angles make 270°.

Estimating an acute angle

  1. The angle is less than 90°.
  2. It is closer to 90° than to 0°.
  3. So it is between 45° and 90° — about 65°.

Answer: A good estimate is about 65°.

Estimating an obtuse angle

  1. The angle is greater than 90°.
  2. It is closer to 90° than to 180°.
  3. 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.