中文（繁體）
中文（简体）
English
Angles and the Angle Sum of a Triangle Paper 1: Basics
Angles and the Angle Sum of a Triangle Paper 1: Basics
Start with right, complementary and adjacent angles, then the angle sums of triangles and quadrilaterals.
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)
- FoundationHow many degrees is a right angle? Can a triangle contain two right angles?
- FoundationTwo angles add up to 90 degrees and one of them is 35 degrees. What is the other?
- FoundationTwo adjacent angles sit on a straight line and one is 40 degrees. Find the other.
- IntermediateA triangle has angles of 60 and 70 degrees. What is the third angle?
- IntermediateWhat is each angle of an equilateral triangle, and why?
- IntermediateOne acute angle of a right-angled triangle is 25 degrees. Find the other acute angle.
- ChallengeWhat is the angle sum of a quadrilateral? If three angles are 100, 90 and 80 degrees, find the fourth.
- ChallengeClassify these angles: 100 degrees, 89 degrees and 180 degrees.
- ChallengeTwo straight lines cross and one angle is 120 degrees. What is the vertically opposite angle?
- Error redoError 10: a student says the angle sum of a triangle is 360 degrees, then gives 90, 50 and 40 degrees. How should you respond?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | A right angle is 90 degrees. A triangle cannot have two right angles, because 90 plus 90 already uses the whole 180 degrees. | Fix 90 degrees as a right angle first, then check whether the remaining angles still have room. |
| 2 | 55 degrees, since 90 minus 35 leaves 55. | Two angles adding to 90 degrees are complementary, so subtract to find the other. |
| 3 | 140 degrees, because adjacent angles on a straight line make a straight angle of 180 degrees. | A straight angle is 180 degrees, so seeing a straight line should bring 180 to mind. |
| 4 | 50 degrees, using the angle sum of 180 and subtracting 60 then 70. | The angle sum of 180 degrees is the rule used most often in this chapter. |
| 5 | 60 degrees each, because the three equal angles share 180 degrees. | Equilateral means three equal angles, so divide rather than subtract. |
| 6 | 65 degrees, since the right angle takes 90 and the two acute angles share the rest. | The two acute angles of a right-angled triangle add to 90 degrees. |
| 7 | The sum is 360 degrees and the fourth angle is 90 degrees. | A quadrilateral splits into two triangles, so the sum is 180 times 2. |
| 8 | 100 degrees is obtuse, 89 degrees is acute and 180 degrees is a straight angle. | The boundaries are 90 and 180; exactly 90 is a right angle and exactly 180 is a straight angle. |
| 9 | 120 degrees, because vertically opposite angles are equal and need no subtraction. | Vertically opposite angles are equal; only adjacent angles are supplementary. |
| 10 | The sum is 180 degrees. Those three angles do add to exactly 180, so the triangle is fine, but the stated sum of 360 is wrong. | Check the total first, then check that every angle is above zero; both steps are needed. |
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.
State the rule, substitute the numbers, then check with a second method.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.