Higher January 2022 Paper 2R Q4

EdexcelHigherCurrent spec4 marksAngles in Polygons

4 The diagram shows a regular octagon \(ABCDEFGH\) and a regular pentagon \(ABIJK\)

Regular octagon ABCDEFGH with regular pentagon ABIJK drawn inside on side AB; angle x is between IB and the dashed line IC

Diagram NOT accurately drawn

Work out the size of the angle \(x\)

(4)

Mark scheme

Scheme	Marks
360 ÷ 8 (= 45) or 360 ÷ 5 (= 72) or 180 – (360 ÷ 8) (= 135) oe or 180 – (360 ÷ 5) (= 108) oe	M1
‘72’ – ‘45’ (= 27) or ‘135’ – ‘108’ (= 27)	M1
\(\dfrac{180 - \text{‘}{27}\text{’}}{2}\ (= 76.5)\)	M1
76.5	A1
	(4)
	(4 marks)

Notes

M1: finding interior or exterior angle of octagon or pentagon
Angles may be seen on diagram – but must be obtuse if interior and acute if exterior.

M1: (dep 1st M1) using a pair of interior or pair of exterior angles to find angle \(IBC\)
Angle may be seen on diagram.