Higher January 2023 Paper 2R Q11

EdexcelHigherCurrent spec4 marksAngles (Including Parallel Lines)Angles in Polygons

Five sides AB, BC, CD, DE, EF of a regular polygon; line RST parallel to CD; line SCU crosses RST at S and passes through C; BC extended to V; angle RSC = 128° and angle UCV = 32°

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 \(RSC = 128°\)
Angle \(UCV = 32°\)

Work out how many sides the polygon has.
Show your working clearly.

(4)

Mark scheme

Scheme	Marks
\(SCD = 128°\) or \(BCS = 32°\) or \(TSC = 180 - 128\;(= 52)\)	M1
eg \((\text{int}\angle =)\;128 + 32\;(= 160)\) or \((\text{ext}\angle =)\;180 - (128 + 32)\;(= 20)\) or \((\text{ext}\angle =)\;\text{``}{52}\text{''} - 32\;(= 20)\)	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.