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P6 Angles & Geometry Questions (with Worked Solutions)
Angle properties, geometric figures, and finding unknown angles in P6 prelim papers. Every question is from a real Singapore P6 preliminary exam, marked instantly, with step-by-step solutions.
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Angles & Geometry questions
Example Angles & Geometry questions
A few real angles & geometry questions from P6 prelim papers. The full set — with marking and progress tracking — is inside SG Maths Exam.
St Nicholas 2025 · Paper 2 · Q7(b) · 2 marks
Using the figure of 2 identical parallelograms ABDH and HDEG and triangle EFG, (b) Find $\angle EFG$.
Worked solution
- $\angle HGE = 360^\circ - 229^\circ - 67^\circ = 64^\circ$. $\angle GEF = 180^\circ - 113^\circ = 67^\circ$. In triangle EFG, $\angle EFG = 180^\circ - 64^\circ - 67^\circ = 49^\circ$.
St Nicholas 2025 · Paper 2 · Q15(d) · 2 marks
On the grid, (d) Draw rectangle DEFG such that it has the same area as triangle CDE. Rectangle DEFG must not overlap with trapezium ABCD and triangle CDE.
Worked solution
- Rectangle DEFG is drawn sharing side DE, with the other side chosen so that its area equals the area of triangle CDE, placed away from the trapezium and triangle.
Nanyang 2025 · Paper 2 · Q15(b) · 2 marks
GAOF is a rhombus and GOEF is a parallelogram. AOE, GOC, FOB, FED and ABCD are straight lines. $\angle OFG = 76^\circ$ and $\angle GAB = 90^\circ$. Find $\angle CDE.
Worked solution
- Using the rhombus and parallelogram properties, $\angle OFG = 76^\circ$ gives the diagonal angle $\frac{76^\circ}{2} = 38^\circ$. Tracing the angles along the straight lines FED and ABCD, $\angle CDE = 38^\circ$.
St Nicholas 2025 · Paper 1 Booklet B · Q24(b) · 1 mark
Using the square grid of points A to F, (b) Pan Ling stood at point B at first. After she turned 90 degrees anti-clockwise, she faced F. Which point was Pan Ling facing at first?
Worked solution
- Turning $90^\circ$ anti-clockwise to face F means she was originally facing $90^\circ$ clockwise from F, which is point C.
Tao Nan 2025 · Paper 2 · Q12(b) · 2 marks
Find $\angle y$.
Ai Tong 2025 · Paper 1 Booklet B · Q26(a) · 1 mark
In the square grid, AB and BC are straight lines.
(a) Measure and write down the size of $\angle ABC$.
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