Angles in Polygons

Topic

Current PowerPoint version

Higher June 2025 Paper 1 Q3

EdexcelCurrent spec4 marksAngles in Polygons

Two sides AB and BC of a polygon meeting at B; AB is vertical, the angle between BC and the extension line at B is 50 degrees, and the angle marked 148 degrees is between AB and that line

Diagram NOT accurately drawn

\(AB\) and \(BC\) are two sides of a regular polygon with \(n\) sides.

Work out the value of \(n\)
Show your working clearly.

(4)

Mark scheme

Scheme	Marks
eg 360 – (148 + 50) (= 162) or 180 – 50 (= 130) or 180 – 148 (= 32)	M1
eg 180 – “162” (= 18) or 148 – “130” (= 18) or 50 – “32” (= 18) or eg 180(\(n\) – 2) = “162”\(n\) or 180(\(n\) – 2) ÷ \(n\) = “162”	M1
eg 360 ÷ “18” or eg (\(n\) =) 360 ÷ (180 − “162”)	M1
Working required Answer: 20	A1
	(4)
	(4 marks)

Notes

M1: for method to interior angle of the polygon or start to the method of finding the exterior angle of the polygon

M1: for method to find the exterior angle or for setting up an equation using sum of interior angles formula

M1: for a complete method

A1: dep on M1

Higher November 2024 Paper 2 Q11

EdexcelCurrent spec5 marksAngles in Polygons

Regular pentagon ABCDE and regular hexagon DEFGHI sharing side DE; the line AF is drawn and angle EAF is marked

Diagram NOT accurately drawn

\(ABCDE\) is a regular pentagon.
\(DEFGHI\) is a regular hexagon.
\(AF\) is a straight line.

Work out the size of angle \(EAF\)

(5)

Mark scheme

Scheme	Marks
int angle of pentagon = (3 × 180) ÷ 5 (= 108) oe or ext angle of pentagon = 360 ÷ 5 (= 72) oe	M1
int angle of hexagon = (4 × 180) ÷ 6 (= 120) or ext angle of hexagon = 360 ÷ 6 (= 60)	M1
360 – (“108” + “120”) (= 132) oe or “60” + “72” (= 132) or (180 – “108”) + (180 – “120”) (= 132)	M1
[180 – (“60” + “72”)] ÷ 2 oe or \(\dfrac{180 - \text{``}{132}\text{''}}{2}\) oe or [180 – (180 – “108”) – (180 – “120”)] ÷ 2 oe	M1
Correct answer scores full marks (unless from obvious incorrect working) Answer: 24	A1
	(5)
	(5 marks)

Notes

M1: allow in working but not if labelled in wrong place on diagram (unless clearly started again)

M1: A fully correct method to find the size of obtuse angle \(AEF\) but not if labelled in wrong place on diagram
[Figures in inverted commas must come from correct working]

M1: A fully correct method to find the size of angle \(EAF\)

[Figures in inverted commas must come from correct working]

A1: cao