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PSLE 2022 · Paper 2 · Q12 Measurement & Geometry · Geometry (angles) 4 marks: 2 + 1 + 1 · long answer (3 parts) difficulty 4 of 5

PSLE 2022 Paper 2, Question 12: Geometry (angles)

The answer

(a) \(\angle ACD = 39^{\circ}\) · (b) \(\angle CDA = 111^{\circ}\) · (c) \(\angle EAB = 99^{\circ}\)

PSLE 2022 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 2022 Paper 2 Mathematics paper. It tests geometry (angles), in the Measurement & Geometry strand. It is worth 4 marks: 2 + 1 + 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 2022 Paper 2 Question 12

Teacher video · 2022 P2 Q12

Step-by-step solution

Figure with the equilateral triangle ACE highlighted, parallel arrows on AB and DC, and 39 and 21 degrees marked — Annotated figure from the GPA worked solution: triangle ACE is equilateral, so each of its angles is 60°.

(a) Triangle DCE is isosceles (\(DC = DE\)) with \(\angle CDE = 138^{\circ}\): \(\angle DCE = (180^{\circ} - 138^{\circ}) \div 2 = 21^{\circ}\). \(\angle ACE = 60^{\circ}\) (equilateral), so \(\angle ACD = 60^{\circ} - 21^{\circ} = 39^{\circ}\).

(b) \(\angle CAE = 60^{\circ}\) and \(\angle DAE = 30^{\circ}\), so \(\angle CAD = 60^{\circ} - 30^{\circ} = 30^{\circ}\). In triangle ACD: \(\angle CDA = 180^{\circ} - 30^{\circ} - 39^{\circ} = 111^{\circ}\).

(c) \(AB \parallel DC\), so \(\angle BAC = \angle ACD = 39^{\circ}\) (alternate angles). \(\angle EAB = \angle CAE + \angle BAC = 60^{\circ} + 39^{\circ} = 99^{\circ}\).

Answer: (a) \(\angle ACD = 39^{\circ}\) · (b) \(\angle CDA = 111^{\circ}\) · (c) \(\angle EAB = 99^{\circ}\)

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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