Angles in Polygons: WJEC GCSE Intermediate November 2016 Unit 1 Q10

Intermediate November 2016 Unit 1 Q10

WJECIntermediateCurrent spec6 marksAngles in Polygons Constructions

10. A regular polygon has exterior angles of 45°.

(a) How many sides does this polygon have? [2]

(b) Each side of this regular polygon is 7 cm.
A sketch of two sides, AB and BC, of the polygon is shown below.

Sketch: AB = 7 cm horizontal; BC rises from B at 45° to the dashed extension of AB beyond B.

Diagram not drawn to scale

Using only a ruler and a pair of compasses, construct an accurate drawing that shows these two sides of the polygon.
The point A has been given.
You must show your construction arcs. [4]

Mark scheme (a)

Scheme	Marks	Comments
\(\dfrac{360}{45}\)	M1	For a clear intention of finding how many 45s in 360.
= 8 (sides)	A1	Accept embedded answers e.g. 360/8 =45 or 45 × 8 = 360 for M1A1.

Mark scheme (b)

Scheme	Marks	Comments
Correct construction of 90°.	B2	Do not penalise if they use their own point A. Use overlay but arcs required for the 3 ‘angle marks’. With sight of accurate ‘method arcs’. For this B2 the construction need not be at point B. (Final B1 will not then be awarded) B1 for sight of ‘method arcs’ but perpendicular line not drawn (Unless intersection of construction arcs for 90° are correctly used to construct the 45° angle. In this case the B2 and B1 are gained)
Correct bisector of 90°.	B1	With sight of accurate ‘method arcs’. F.T. ‘their 90°’.
AB = 7cm AND BC = 7cm	B1	Allow ± 0·2cm. Do not penalise if the line AB is extended as long as the position of point B is unambiguous. (Allow labelling of points B and C to be missing if end points are unambiguously identifiable.) If all marks gained but angle ABC = 45°, penalise −1.