Foundation June 2024 Paper 3 Q20
20 \(ABC\) and \(BCD\) are isosceles triangles.
\(AB = BC = CD\)
Angle \(CAB\) = 81°
Angle \(BCD = 4 \times\) angle \(ABC\)
Find
the size of angle \(ABC\) : the size of angle \(CBD\)
Give your answer in the form \(1 : n\)
You must show all your working. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| 1 : 3 | M1 | for method to find angle \(ABC\), eg \(180 - 2 \times 81\ (= 18)\) oe |
| M1 | for method to find angle \(BCD\), eg \(\text{``}18\text{''} \times 4\ (= 72)\) | |
| M1 | for method to find angle \(CBD\), eg \(\dfrac{180 - \text{``}72\text{''}}{2}\ (= 54)\) | |
| M1 | (dep M3) for writing as ratio, eg "18" : "54" or for an answer of \(1 : 3n\) or \(3 : 1\) | |
| A1 | (dep M3) for 1 : 3 from correct working |
Additional guidance
Award first 3 marks for angles 18, 72, 54 marked on diagram provided not ambiguous
Accept \(n = 3\)
1 : 3 or \(n = 3\) without working scores 0 marks