Q1.
A student used a protractor to measure the angles as shown (∠U = 35°, ∠V = 80°, ∠W = 70°, ∠X = 150°, ∠Y = 120°, ∠Z = 85°). In each figure, identify the incorrect usage(s) of the protractor and discuss how the reading could have been made and think how it can be corrected.
Answer
Look at each picture and ask the same three questions: Is the centre on the vertex? Is one arm on the 0 line? Which scale was read?
| Figure | What has gone wrong | How to correct it |
|---|---|---|
| ∠U = 35° | The vertex of the angle is at the right-hand end of the base line, not at the centre of the protractor. | Slide the protractor left until its centre mark sits exactly on the vertex. |
| ∠V = 80° | The protractor is tilted; neither arm of the angle lies along the 0 line. | Turn the protractor until one arm runs exactly along the base line through 0. |
| ∠W = 70° | Only one arm is drawn, so it cannot be seen which side of the base line is the second arm — and the reading has been taken from the wrong set of numbers. | Draw both arms, then follow the scale that starts at 0 on the base arm (here it gives 110°, not 70°). |
| ∠X = 150° | The protractor is tilted and its centre is away from the vertex, so the arms cross the scale at the wrong marks. | Centre on the vertex first, then rotate so that one arm is on 0. |
| ∠Y = 120° | The line drawn does not pass through the centre of the protractor — the vertex is off the centre mark. | Move the protractor so that the vertex and the centre coincide. |
| ∠Z = 85° | The protractor is placed upside down and tilted, so the numbers run the wrong way and no arm is at 0. | Put the flat edge along one arm with the numbers the right way up, then read. |
In short, every wrong reading comes from one of three mistakes:
- The centre of the protractor is not on the vertex.
- No arm lies along the 0 line (so the reading must be corrected by subtraction).
- The wrong scale was read — the inner numbers were used with an arm set on the outer 0, or the other way round.
Wrong scale used → true angle = 180° − wrong reading
Example: reading 150° when the true angle is 30°
Example: reading 150° when the true angle is 30°
Tip: before reading, always guess the angle first. A guess of “about 40°” saves you from writing 140°.