4MA0 Higher January 2014 Paper 4 Q19

EdexcelHigherOld spec3 marksAngles in Polygons

Part of a regular polygon with the interior angle and exterior angle at a vertex marked

Diagram NOT accurately drawn

The diagram shows part of a regular polygon.
The interior angle and the exterior angle at a vertex are marked.
The size of the interior angle is 7 times the size of the exterior angle.

Work out the number of sides of the polygon.

(3)

Mark scheme

Scheme	Marks
180 ÷ ( 1 + 7) (= 22.5)	M1
360 ÷ “22.5”	M1ft
16	A1
	(3)
	(3 marks)

Notes

M1ft: dep M2 for \(\dfrac{180(n - 2)}{n} = \dfrac{7 \times 180}{8}\) or \(\dfrac{7 \times 360}{n}\)

or M2 for \(360 \div \dfrac{180}{(1 + 7)}\)

A1: cao