4400 Higher November 2006 Paper 4 Q15

EdexcelHigherOld spec5 marksAngles in Polygons

Equilateral triangle ABC with angle 60 degrees at A; line AD from A; regular polygons on sides AB and AC meet at A

Diagram NOT accurately drawn

The sides of an equilateral triangle \(ABC\) and two regular polygons meet at the point \(A\).
\(AB\) and \(AD\) are adjacent sides of a regular 10-sided polygon.
\(AC\) and \(AD\) are adjacent sides of a regular \(n\)-sided polygon.
Work out the value of \(n\).

(5)

Mark scheme

Scheme	Marks
\(\dfrac{180 \times (10 - 2)}{10}\) or \(180 - \frac{360}{10}\) or \(\frac{360}{10}\)	M1
144 36	A1
180 − [360 − (60 + 144)] or 24 60 − 36 (= 24)	M1
\(\dfrac{360}{\text{“}24\text{”}}\)	M1
15	A1
	(5)
	(5 marks)

Notes

M1: 360 − 204 = 156

M1: \(180 \times (n - 2)/n = 156\) or \(180 - 360/n = 156\) or 2340/15 = 156

A1: cao