Angles in Polygons: WJEC GCSE Higher June 2019 Unit 1 Q3

Higher June 2019 Unit 1 Q3

WJECHigherCurrent spec6 marksAngles in Polygons

3. In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

A regular octagon with centre \(O\) is shown below.

Regular octagon ABCDEFGH with centre O; the line OA is drawn and angle OAB is marked

Diagram not drawn to scale

Calculate the exact size of \(O\hat{A}B\).
You may choose to draw additional lines on the diagram to help you.
You must show all your working. [4 + 2 OCW]

Mark scheme

Scheme	Marks	Comments
		Answers/working may be seen on diagram.
(Angle AÔB or exterior angle =) \(\dfrac{360}{8}\)(°)	M1
= 45(°)	A1	Sight of 45 (even e.g. OÂB = 45) gains M1A1.
(OÂB =) \(\dfrac{180 - 45}{2}\)	M1	FT ‘their 45’ (but not 60°).
= 67·5(°)	A1
Organisation and Communication.	OC1	For OC1, candidates will be expected to: present their response in a structured way explain to the reader what they are doing at each step of their response lay out their explanation and working in a way that is clear and logical write a conclusion that draws together their results and explains what their answer means
Accuracy of writing.	W1	For W1, candidates will be expected to: show all their working make few, if any, errors in spelling, punctuation and grammar use correct mathematical form in their working use appropriate terminology, units, etc

3. Alternative method 1

Scheme	Marks	Comments
(Sum of interior angles =)(8 – 2)×180° or equivalent	M1
= 1080(°)	A1	(Interior angle =) 135(°) implies M1A1
(OÂB =) ½ × (1080 ÷ 8)	M1	FT ‘their interior angle sum’ (≠ 1440)
= 67·5(°)	A1

3. Alternative method 2

Scheme	Marks	Comments
(Using 16 right-angled triangles)
(Angle at O =) 360 / 16	M1
= 22·5(°)	A1
(OÂB =) 180 – 90 − 22·5	M1	FT ‘their 22·5’.
= 67·5(°)	A1