Angles
Measuring and drawing angles
An angle measures an amount of turn. We name angles by their size and use a protractor to measure and draw them accurately.
Naming angles by their size
• An acute angle is between 0° and 90°. • A right angle is exactly 90° (a quarter turn). • An obtuse angle is between 90° and 180°. • A straight line is 180° (a half turn). • A reflex angle is between 180° and 360°. • A full turn is 360°.
Using a protractor
A protractor is a flat object with 0° to 360° marked around its edge. Put the centre of the protractor on the point of the angle, and line up one arm exactly with 0°. When the angle opens clockwise from 0°, read the OUTSIDE numbers. When it opens anticlockwise from 0°, read the INSIDE numbers. Always estimate the angle first, then measure.
Drawing an angle
Start with a horizontal line. Put the centre of the protractor on one end, with the line at 0°. Count round to the size you want and mark a small line. Take the protractor away, join your mark to the end of the line, then draw an arc and write the size.
Angles that fit together
Angles on a straight line add up to 180°, so if you know one you can subtract from 180° to find the other. Angles that meet all the way round a point add up to 360°, so you only need to measure one to work out the reflex angle beside it.
Worked examples
Naming an angle by its size
- Look at an angle that measures 50°.
- A right angle is 90°. Compare: 50° is less than 90°.
Answer: 50° is an acute angle.
Measuring an angle with a protractor
- Estimate the angle first — about 45°.
- Place the centre of the protractor on the point and line one arm up with 0°.
- The angle opens clockwise, so read the outside numbers.
Answer: The angle measures 50°.
Drawing an angle of 120°
- Draw a horizontal line and put the protractor centre on the right end.
- Measure 120° clockwise using the outside numbers and mark the point.
- Join the mark to the end of the line and label the angle.
Answer: You have drawn an angle of 120° (an obtuse angle).
Finding a missing angle on a straight line
- Two angles sit on a straight line and one of them is 142°.
- Angles on a straight line add up to 180°.
- Subtract: 180° − 142°.
Answer: The missing angle is 38°.
Where you see this in real life
- An architect measuring and drawing the angles of a roof and staircase.
- Checking that a wheelchair ramp is no steeper than 20°.
- A photographer turning a camera through an angle to point at a different subject.
Key words
- Protractor
- A flat tool marked from 0° to 360° used to measure and draw angles.
- Acute angle
- An angle between 0° and 90°.
- Right angle
- An angle of exactly 90°, a quarter turn.
- Obtuse angle
- An angle between 90° and 180°.
- Reflex angle
- An angle between 180° and 360°.
- Clockwise
- Turning the same way as the hands of a clock.