PSLE geometry and angles questions with worked answers
Geometry questions give your child a figure and expect a chain of angle facts, each one stated. The usual loss is a wrong total, such as 360° where 180° belongs, or stopping one step before the angle the question asked for.
What the PSLE tests in geometry & angles
- Angles on a straight line, at a point, and vertically opposite angles
- Sum of angles in a triangle, and properties of isosceles, equilateral and right-angled triangles
- Properties of the parallelogram, rhombus and trapezium, and the sum of angles in a quadrilateral
- Finding unknown angles in figures made of several shapes
- Nets of cubes, cuboids, prisms and pyramids
Where children lose the most marks
- Unknown angles that need three or more facts in a row, across overlapping triangles and quadrilaterals
- Isosceles triangles hidden inside a figure, shown only by equal side marks
- Parallelogram and trapezium questions that rely on angles between parallel lines adding to 180°
A PSLE-style question, worked
In triangle ABC, AB = AC and ∠BAC = 40°. The side BC is extended to a point D, so that B, C and D lie on a straight line. Find ∠ACD.
- AB = AC, so triangle ABC is isosceles and ∠ABC = ∠ACB
- ∠ACB = (180° − 40°) ÷ 2 = 70° (angles in a triangle)
- ∠ACD = 180° − 70° = 110° (angles on a straight line)
Why 70° is wrong: The child found ∠ACB inside the triangle and stopped. ∠ACD is the angle outside the triangle on the straight line BD, so it is 180° − 70°.
Free PSLE geometry & angles questions with answers
Careless mistakes to watch in geometry & angles
Questions parents ask
Does my child need to write reasons for angles in the PSLE?
Clear working earns method marks in structured questions. Writing the fact used, such as "angles on a straight line", helps your child and the marker follow each step.
Are nets still tested in PSLE Maths?
Yes. Identifying the net of a solid, and which faces meet when it is folded, commonly appears as a Paper 1 question.
Can my child measure angles with a protractor instead of calculating?
Only when the question asks for a measurement. Figures in the PSLE are often not drawn to scale, so unknown angles must be calculated.
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