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S5 Maths: Angles in Circles: Paper 1 (basics)
S5 Maths: Angles in Circles: Paper 1 (basics)
Ten items that start from the doubling relation and add semicircles, equal angles in the same segment and cyclic quadrilaterals.
Direct answers Items 1-3: 40, 70, 90 degrees. Items 4-6: 52, 85, 55 degrees. Items 7-9: x = 25 with 85 degrees, 260 degrees, 80 degrees. Item 10: 20 degrees is wrong; the answer is 80 degrees.
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: S5 Maths: Angles in Circles |
| Level | Basics |
02 Questions (10 items)
- FoundationThe central angle AOB = 80 degrees and C lies on the major arc AB. Find the angle ACB in the circle.
- FoundationThe inscribed angle ACB = 35 degrees and it stands on the arc AB. Find the central angle AOB.
- FoundationAB is a diameter of the circle and C is a point on the circle. Find the angle ACB.
- IntermediateThe points C and D lie in the same segment and the angle ACB = 52 degrees. Find the angle ADB.
- IntermediateABCD is a cyclic quadrilateral and the angle at A is 95 degrees. Find the angle at C.
- IntermediateAB is a diameter and the angle ABC = 35 degrees. Find the angle BAC.
- ChallengeThe central angle AOB = 3x + 10 and the inscribed angle ACB = x + 30 on the same arc. Find x and the central angle.
- ChallengeThe central angle AOB = 100 degrees. Find the reflex angle AOB at the same centre O.
- ChallengeOn the same circle the arcs AB and BC are in the ratio 3 : 2 and the angle AOB = 120 degrees. Find the angle BOC.
- Error redoA student sees an inscribed angle of 40 degrees and writes the central angle on the same arc as 20 degrees. What is wrong, and what is the correct value?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 40 degrees | On the same arc the inscribed angle is half the central angle, so 80 / 2 = 40 degrees. |
| 2 | 70 degrees | The central angle is twice the inscribed angle, so 35 x 2 = 70 degrees. |
| 3 | 90 degrees | The angle in a semicircle is a right angle, so the angle ACB is 90 degrees. |
| 4 | 52 degrees | Angles in the same segment are equal, so the angle ADB is 52 degrees. |
| 5 | 85 degrees | Opposite angles of a cyclic quadrilateral are supplementary, so 180 – 95 = 85 degrees. |
| 6 | 55 degrees | The angle ACB is 90 degrees, so the angle BAC is 90 – 35 = 55 degrees. |
| 7 | x = 25 and the central angle is 85 degrees | From 3x + 10 = 2(x + 30) we get x = 25, so the central angle is 85 degrees. |
| 8 | 260 degrees | The reflex angle completes the full turn, so 360 – 100 = 260 degrees. |
| 9 | 80 degrees | Arcs are proportional to central angles, so 120 x 2 / 3 = 80 degrees. |
| 10 | 20 degrees is wrong; it should be 80 degrees | The central angle is twice the inscribed angle, so dividing by 2 reverses the relation. |
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.
Mark the central angle on the diagram first, then decide whether to double or halve.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.