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Angles and the Angle Sum of a Triangle Paper 3: Challenge
Angles and the Angle Sum of a Triangle Paper 3: Challenge
Ratios and multiples, a regular hexagon and obtuse classification, training multi-step reasoning.
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)
- FoundationOne angle of a triangle is twice another and the third is 60 degrees. Find the two unknown angles.
- FoundationAn isosceles triangle has a base angle of 35 degrees. Find the apex angle and say whether the triangle is obtuse.
- FoundationThe three angles of a triangle are in the ratio one to two to three. Find them.
- IntermediateOne angle of a quadrilateral is 120 degrees and the other three are equal. Find them.
- IntermediateTwo straight lines cross and one angle is 65 degrees. Find all four angles.
- IntermediateTwo angles of a triangle are 40 and 60 degrees. Find the exterior angle at the third vertex using two methods.
- ChallengeIn a right-angled triangle one acute angle is four times the other. Find both.
- ChallengeWhat is the angle sum of a regular hexagon, and what is each interior angle?
- ChallengeA triangle has angles of 100 and 45 degrees plus a third. Find it and classify the triangle.
- Error redoError 10: a quadrilateral has angles of 110, 100 and 90 degrees and a student subtracts from 180, getting a negative. What is the right answer?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 40.0 and 80.0 degrees: with x plus 2x plus 60 equal to 180, x comes out at 40. | An equation handles the ratio far faster than guessing values. |
| 2 | The apex is 110 degrees, above 90, so the triangle is obtuse-angled. | Classify by the largest angle, not by a base angle. |
| 3 | 30.0, 60.0 and 90.0 degrees, since 180 divides into six parts of 30. | Turn the ratio into a number of parts before finding one part. |
| 4 | 80.0 degrees each: 360 minus 120 leaves 240, which splits three ways. | The quadrilateral rule gives 360, so subtract before dividing by three. |
| 5 | Two angles measure 65 degrees and two measure 115, since opposite angles are equal and adjacent ones are supplementary. | The four angles must total 360, which makes a quick check. |
| 6 | The exterior angle is 100 degrees: either add 40 and 60, or find 80 for the third angle and subtract from 180. | Both routes must give the same number before the idea is secure. |
| 7 | 18.0 and 72.0 degrees: the acute angles share 90 degrees, which splits into five parts of 18.0. | The two acute angles are complementary, so work from 90 rather than 180. |
| 8 | The sum is 720 degrees and each angle is 120.0, since a hexagon splits into four triangles. | The angle sum of a polygon is 180 times the number of sides minus two. |
| 9 | The third angle is 35 degrees and the largest angle is 100, so the triangle is obtuse-angled. | Classification uses the largest angle only; the other two do not change the name. |
| 10 | The fourth angle is 60 degrees; a quadrilateral uses 360 and 180 belongs to triangles. | A negative result signals the wrong rule, so go back and check at once. |
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.
Set the unknown as x or as parts, write the equation, then check against 180.Tutor Registration →
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