The answer
\(45^{\circ}\), \(27^{\circ}\), \(108^{\circ}\)
O-Level E-Math 2015 Paper 1 Question 11 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 11 of the O-Level E-Math 2015 Paper 1. It tests form and solve a linear equation from a worded geometric condition, in the Equations & inequalities area. It is worth 3 marks. 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.
Let the first angle be \(x^{\circ}\). Then the second angle is \((x - 18)^{\circ}\) and the third is \(4(x - 18)^{\circ}\). The angles of a triangle sum to \(180^{\circ}\): \[x + (x - 18) + 4(x - 18) = 180 \Rightarrow 6x - 90 = 180 \Rightarrow 6x = 270 \Rightarrow x = 45.\] First angle \(= 45^{\circ}\), second \(= 45 - 18 = 27^{\circ}\), third \(= 4 \times 27 = 108^{\circ}\). (Check: \(45 + 27 + 108 = 180^{\circ}\).)
Answer: \(45^{\circ}\), \(27^{\circ}\), \(108^{\circ}\)
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 form and solve a linear equation from a worded geometric condition question from Equations & inequalities, worth 3 marks.
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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