Discover Mathematics P4: Term 2, Unit 13, Lessons 5–8
GoalMeasure an angle with a protractor in four steps, checking the answer with an estimate.
New words
vertex · the point where the two arms of the angle meetarm · one of the two rays that make an angleestimate · a sensible guess before measuring, for example “about 100°”
Explanation
Follow four steps. First, estimate: is the angle acute, right or obtuse? Second, put the centre mark of the protractor on the vertex. Third, turn the protractor until the baseline lies exactly along one arm. Fourth, look where the other arm crosses the scale and read the scale that starts at 0° on the arm along the baseline. Compare with your estimate: an acute angle must read less than 90° and an obtuse angle more than 90°. If the arms are too short to reach the scale, extend them with a ruler. The same steps work when the angle opens to the left: then the 0° of the left scale is on the baseline arm.
1. Estimate the angle→2. Centre mark on the vertex→3. Baseline along one arm→4. Read the scale from 0°
Worked examples
Measure this angle. Estimate: it is acute. Put the centre mark on the vertex and the baseline along the right arm. The other arm crosses the scale at 65°. This agrees with the estimate (less than 90°), so the angle is 65°.
Measure an angle that opens to the left. Estimate: it is obtuse. The baseline lies along the left arm, so we read the scale that starts at 0° on the left. The other arm crosses at 125°. It is more than 90°, as the estimate says, so the angle is 125°.
Which reading makes sense? The angle is wider than a square corner, so it is obtuse. The two scales show 30° and 150°. Only 150° is more than 90°, so the angle is 150°. Checking with an estimate saves us from reading the wrong scale.
Class activity
Angle measuring. Draw five angles with a ruler on plain paper, with arms about 8 cm long. For each one, write your estimate (acute or obtuse, and a number such as 60°), then measure with a protractor and write the real size. How close were your estimates? Swap papers with a friend and check each other.
Practice
1
Read the angle in the picture. The baseline is on the right arm.
120°. The angle is obtuse, so it is more than 90°.
2
Read the angle. The baseline is on the left arm.
75°. The angle is acute and the scale from the left gives 75°.
3
Why is it a good idea to estimate before measuring?
The estimate tells us whether the angle is less or more than 90°, so we can tell which of the two scale readings is the sensible one.
4
The arms of an angle are too short to reach the scale. What do you do?
Extend the arms with a ruler and then measure. The size of the angle does not change.
5
Aya measures an obtuse angle and reads 55°. What should she do?
Check the scale: an obtuse angle is more than 90°. She read the wrong scale. The right reading is 180° − 55° = 125°.
