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Angles and the Angle Sum of a Triangle Paper 4: Error Clinic
Angles and the Angle Sum of a Triangle Paper 4: Error Clinic
Ten real slips taken apart, from a triangle totalling 190 to a misread protractor.
Direct answers Answers and explanations for all ten questions
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: P4 Angles and the Angle Sum of a Triangle |
| Level | P1 |
02 Questions (10 items)
- FoundationError 1: a triangle is written with angles 90, 60 and 40 degrees, which total 190. Where is the mistake and what should the third angle be?
- FoundationError 2: an isosceles triangle has base angles of 70 degrees and a student answers 110 for the apex. What is correct?
- FoundationError 3: two adjacent angles on a straight line, one of 130 degrees, and a student says the other is also 130. Why is that wrong?
- IntermediateError 4: a student claims each angle of an equilateral triangle is 90 degrees. What is right, and how should it be remembered?
- IntermediateError 5: a quadrilateral has angles of 110, 100 and 90 degrees and a student subtracts from 180, getting a negative. Find the fourth angle.
- IntermediateError 6: two lines cross at 65 degrees and a student says the vertically opposite angle is 115. What is right, and why the error?
- ChallengeError 7: the acute angles of a right-angled triangle are written as 30 and 50 degrees, totalling 80. What should the second be?
- ChallengeError 8: reading the wrong scale on a protractor turns 120 degrees into 60. What is the difference and how is it avoided?
- ChallengeError 9: a triangle with angles 45, 45 and 90 is called equilateral by a student. What is the correct name?
- Error redoError 10: a triangle has angles 70, 45 and 65 degrees and the exterior angle at the 70 degree vertex is written as 45 minus 65. What is correct?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | A triangle totals exactly 180, so 190 is impossible; the third angle should be 30. | Add the three angles first: anything above 180 means a copying or arithmetic slip. |
| 2 | The apex is 40 degrees, since 180 minus both 70s leaves 40. | Answering 110 subtracts only one base angle, but there are two. |
| 3 | The other angle is 50 degrees: adjacent angles on a line are supplementary, and only vertically opposite angles are equal. | Equality and supplementary are different claims, and position decides which applies. |
| 4 | Each angle is 60 degrees, from dividing the 180 degree sum by three. | 90 is a right angle, and three right angles could never total 180. |
| 5 | The fourth angle is 60 degrees, because a quadrilateral sums to 360 and 300 is already used. | A negative answer means 180 was used where 360 was required. |
| 6 | The vertically opposite angle is also 65; the 115 figure belongs to the adjacent angle. | Opposite angles face each other across the crossing while adjacent ones sit side by side. |
| 7 | It should be 60 degrees, since the acute angles must total 90. | The check is simply adding the two acute angles and seeing whether they make 90. |
| 8 | The difference is 60 degrees; start from the scale that opens with the angle and cross-check on the other ring. | The two rings always add to 180, which makes the cross-check easy. |
| 9 | It is an isosceles right-angled triangle; equilateral needs all three angles at 60 degrees. | Isosceles needs two equal angles while equilateral needs three, a stricter condition. |
| 10 | The exterior angle is 110 degrees, equal to 45 plus 65 or to 180 minus 70. | Both valid rules add, or subtract from 180; subtracting one interior angle from another is not one of them. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
Name the faulty step, give the correct method, then verify by addition.Tutor Registration →
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