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Angles and the Angle Sum of a Triangle Paper 2: Intermediate
Angles and the Angle Sum of a Triangle Paper 2: Intermediate
Isosceles triangles, adjacent angles, exterior angles and clock hands, with every value checked.
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)
- FoundationAn isosceles triangle has an apex angle of 40 degrees. Find each base angle.
- FoundationAn isosceles triangle has base angles of 55 degrees. Find the apex angle.
- FoundationTwo adjacent angles lie on a straight line and one is 115 degrees. Find the other.
- IntermediateA triangle has angles of 45 and 65 degrees. Find the third angle and classify the triangle.
- IntermediateThree angles of a quadrilateral are 95, 85 and 100 degrees. Find the fourth.
- IntermediateTwo interior angles of a triangle are 40 and 65 degrees. Find the exterior angle at the third vertex.
- ChallengeAt three o’clock, what is the angle between the hour hand and the minute hand?
- ChallengeA triangle has two equal angles and a third angle of 30 degrees. Find the equal angles.
- ChallengeA quadrilateral has two right angles and the other two are equal. Find them.
- Error redoError 10: an isosceles triangle has an apex angle of 80 degrees and a student answers 100 degrees for each base angle. What went wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 70 degrees each: subtract 40 from 180 and halve the remainder. | The base angles of an isosceles triangle are equal, so subtract first and divide second. |
| 2 | 70 degrees, since the two base angles use 110 and 180 minus 110 leaves 70. | There are two base angles, so multiply by two before subtracting. |
| 3 | 65 degrees, because adjacent angles on a straight line are supplementary. | Adjacent angles are supplementary while vertically opposite angles are equal; keep the two apart. |
| 4 | 70 degrees, and all three angles are acute, so it is an acute-angled triangle. | Find the missing angle first, then classify by the largest angle. |
| 5 | 80 degrees, taking 360 minus the 280 already used. | Use 360 for a quadrilateral; 180 belongs to triangles only. |
| 6 | 105 degrees: the exterior angle equals the sum of the two remote interior angles. | Both methods, adding the remote angles or subtracting the adjacent one, must agree. |
| 7 | 90 degrees, because the hands point at 12 and 3, which is a right angle. | Each of the twelve gaps on a clock face is 30 degrees, so three gaps make 90. |
| 8 | 75 degrees each: 180 minus 30 leaves 150, then halve it. | Two equal angles means an isosceles triangle, so the same divide-by-two method applies. |
| 9 | 90 degrees each, so all four angles are right angles and the shape is a rectangle or a square. | The result identifies the shape, not just the number. |
| 10 | The student forgot to halve. Each base angle is 50 degrees, and 80 plus 50 plus 50 gives 180. | Add the three angles as a check and the slip shows up 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.
Decide the relationship first, then choose subtraction or division, then add the angles as a check.Tutor Registration →
Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.