The answer
(a) \(135^{\circ}\)
(b) all four sides equal
(c) \(75^{\circ}\)
O-Level E-Math 2022 Paper 1 Question 7 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 7 of the O-Level E-Math 2022 Paper 1. It tests interior angle of a regular polygon, in the Angles & polygons / Congruence & similarity area. It is worth 5 marks: 2 + 2 + 1. It is a worded / diagram-based question, so open your Ten-Year Series (TYS) or the official paper at this question, then follow our full worked solution below.
(a) Interior angle of a regular octagon \(= \dfrac{(8 - 2) \times 180^{\circ}}{8} = 135^{\circ}\). So angle \(BCD = 135^{\circ}\).
(b) \(BC\) and \(CD\) are sides of the regular octagon, so \(BC = CD\). \(JB\) is a side of the square \(ABJL\), so \(JB =\) octagon side; and \(DJ\) also equals the octagon side (it closes the quadrilateral onto the square/triangle construction). Hence \(BC = CD = DJ = JB\), all four sides equal, so \(BCDJ\) is a rhombus.
(c) The angles around point \(J\) add to \(360^{\circ}\): the rhombus angle at \(J\) (\(= 135^{\circ}\), equal to angle \(BCD\), opposite angles of a rhombus), the square's right angle (\(90^{\circ}\)) and the equilateral triangle's angle (\(60^{\circ}\)). So angle \(KJD = 360^{\circ} - 135^{\circ} - 90^{\circ} - 60^{\circ} = 75^{\circ}\).
Answer: (a) \(135^{\circ}\)
(b) all four sides equal
(c) \(75^{\circ}\)
Same structure, different numbers
Swap the constants, dress a quadratic as a length, hide a derivative inside an integral, and a student sees a brand new problem. The structure underneath is the same, and so is the method. Once a student can name the structure, a whole row of questions that look different start to open the same way.
That is where marks really leak: in choosing the method, not in the algebra that follows. We call it Lock and Key, name the lock, then the key follows.
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Genius Plus Academy · O-Level & IP Mathematics
Our O-Level E-Math tuition trains the same recognise-the-structure method these worked solutions show, taught by a team that has marked these papers for years. It runs within our weekly Secondary Math programme, Sec 1 to 4 and IP.
It is a interior angle of a regular polygon question from Angles & polygons / Congruence & similarity, worth 5 marks: 2 + 2 + 1.
Yes. IP (Integrated Programme) schools teach the same O-Level Mathematics content; they just sequence it differently and set their own internal exams, so these worked solutions apply to IP students too.
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