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Methodist Girls' School (Primary) 2025 P6 Maths Prelim — Paper 1 Booklet A Q15 Solution

Paper 1 Booklet A · Q15 · 2 marks · Angles

Question

In the figure, ABCD is a square. AC and BD are straight lines. BE = BF. Find $\angle CEF$.

1. 67.5°
2. 45°
3. 30°
4. 22.5°

Answer: 4

Worked solution

$\text{In square ABCD, diagonals AC and BD meet at right angles, each making } 45^{\circ} \text{ with sides}$
$\triangle BEF \text{ is isosceles with } BE = BF$
$\angle EBF = 45^{\circ}$
$\angle BEF = \angle BFE = \frac{180^{\circ} - 45^{\circ}}{2} = 67.5^{\circ}$
$\angle CEF = 90^{\circ} - 67.5^{\circ} = 22.5^{\circ}$

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