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PSLE 2018 · Paper 2 · Q12 Measurement & Geometry · Geometry (angles) 4 marks: 3 + 1 · long answer (2 parts) difficulty 3 of 5

PSLE 2018 Paper 2, Question 12: Geometry (angles)

The answer

(a) \(126^{\circ}\) · (b) ABDE ( is not ) a parallelogram because AB ( is not ) parallel to ED

PSLE 2018 Paper 2 Question 12 · Verified worked solution by the Genius Plus Academy teaching team

What this question tests

This is Question 12 of the PSLE 2018 Paper 2 Mathematics paper. It tests geometry (angles), in the Measurement & Geometry strand. It is worth 4 marks: 3 + 1. Open your copy of the paper at this question, then follow our full worked solution below.

Watch the walkthrough

Video: a Genius Plus Academy teacher solving PSLE 2018 Paper 2 Question 12

Teacher video · 2018 P2 Q12

Step-by-step solution

Trapezium annotated with 27° alternate angles at C and A and the isosceles tick marks — Annotated figure from the GPA worked solution (the 53° at D is not needed for part (a)).

(a) \(\angle BCA = \angle CAE = 27^{\circ}\) (alternate angles, \(BD \parallel AE\)). Triangle ABC is isosceles (\(AB = BC\)), so \(\angle BAC = \angle BCA = 27^{\circ}\). \(\angle ABC = 180^{\circ} - 27^{\circ} - 27^{\circ} = 126^{\circ}\) (angle sum of triangle).

(b) If \(AB \parallel ED\), then \(\angle ABD\) would equal \(180^{\circ} - 53^{\circ} = 127^{\circ}\) (co-interior with \(\angle BDE\)); but \(\angle ABD = 126^{\circ} \neq 127^{\circ}\), so AB is not parallel to ED and ABDE is not a parallelogram.

Answer: (a) \(126^{\circ}\) · (b) ABDE ( is not ) a parallelogram because AB ( is not ) parallel to ED

Same structure, different costume

A question is hard because of its structure, not its story.

Change egg tarts to badges, a tank to two tanks, a ring of card to a folded sheet, and a child sees a brand new problem. The lock underneath is the same, and so is the key. Once a student can name the structure, a whole row of questions that look different start to open the same way.

It is also where marks really leak. Across fourteen years of papers, the marks lost in PSLE math leak at the reading far more than at the arithmetic, which is exactly why recognising the structure fixes them. We call this Lock and Key: name the lock, then the key follows.

See what the paper rewards → The hardest questions, shown working →

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