Foundation January 2023 Paper 2R Q25
25
Diagram NOT accurately drawn
\(AB\), \(BC\), \(CD\), \(DE\) and \(EF\) are five sides of a regular polygon.
\(RST\), \(SCU\) and \(BCV\) are straight lines.
\(RST\) is parallel to \(CD\)
Angle \(RSC = 128^\circ\)
Angle \(UCV = 32^\circ\)
Work out how many sides the polygon has.
Show your working clearly.
(4)
| Scheme | Marks |
|---|---|
| \(SCD = 128^\circ\) or \(BCS = 32^\circ\) or \(TSC\) = 180 – 128 (= 52) | M1 |
| eg (int∠ =)128 + 32(=160) or (ext∠ =)180 – (128 + 32)(= 20) or (ext∠ =)“52” – 32(= 20) | M1 |
| eg \(180(n - 2) = \text{“}160\text{”}n\) or 360 ÷ “20” | M1 |
| Working required Answer: 18 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: angles need to be identified or may be seen marked on the diagram
M1: (dep on previous M1) for method to find the size of one interior or exterior angle, may be seen marked on the diagram.
M1: for setting up an equation for the sum of interior angles or 360 ÷ “20”
A1: dep on M2
M2 for (\(BCD\) =) 128 + 32 (= 160) or (\(DCV\) =) 52 – 32 (= 20) (may be seen marked on the diagram). To award these marks 160 or 20 must be clearly used or identified as the interior or exterior angle.