Foundation June 2025 Paper 1 Q24
24 \(AB\), \(BC\), \(CD\) and \(DE\) are four sides of a regular polygon with \(n\) sides.
\(BCX\) is an equilateral triangle.
\(CDYX\) is a square.
Work out the value of \(n\).
You must show all your working. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 12 | P1 | for (interior angle =) \((180 \div 3) + (360 \div 4)\ (= 150)\) |
| P1 | for (exterior angle =) \(180 - \text{``}150\text{''}\ (= 30)\) or for \(\text{``}150\text{''} = \dfrac{(n-2) \times 180}{n}\) oe | |
| P1 | for \(360 \div \text{``}30\text{''}\) or for a correct process to solve the equation as far as \(\text{``}30\text{''}n = 360\) | |
| A1 | cao |
Additional guidance
150 may be seen on diagram.
May be seen on diagram
Exterior angle of 30 implies P1P1
A correct answer with no supportive working gets 0 marks
Minimum supportive working is P1P1
or
Trials of interior angle sum
Finding \(1800 \div 150 = 12\) oe with 12 as answer scores P1P1P1A1