Angles (Including Parallel Lines): Eduqas GCSE Foundation November 2020 Paper 1 Q14

Foundation November 2020 Paper 1 Q14

EduqasFoundationCurrent spec6 marksAngles (Including Parallel Lines)

14.

(a)

Diagram not drawn to scale

Show that \(AB\) and \(CD\) are not parallel.
Give a reason for each step of your answer. [2]

(b)

Diagram not drawn to scale

(i) Calculate the value of \(x\).
Give reasons and calculations to support your answer. [3]

\(x\) = ……… °

(ii) Write down the mathematical name for triangle \(PQR\).
Give a reason for your answer. [1]

Mark scheme (a)

Scheme	Marks	Comments
\(B\hat{F}G\) indicated as 94° or 104° OR \(C\hat{G}F\) indicated as 94° or 104° OR \(A\hat{F}G\) indicated as 76° or 86° and a correct value of another suitable angle indicated OR \(D\hat{G}F\) indicated as 76° or 86° and a correct value of another suitable angle indicated	E1	Any one of these, ignoring others; may be marked on diagram; if not marked on diagram must be correctly described e.g. using 3 letters or marking \(x\) on diagram and finding \(x\) in answer space
Clear and correct reasoning using correct angles e.g. \(B\hat{F}G\) or \(C\hat{G}F\) Corresponding angles should be equal or Vertically opposite angles should be equal \(C\hat{G}F\) and \(B\hat{F}G\) or \(A\hat{F}G\) and \(D\hat{G}F\) Alternate angles should be equal \(A\hat{F}G\) and \(C\hat{G}H\) or \(B\hat{F}E\) and \(B\hat{F}G\) or \(B\hat{F}E\) and \(D\hat{G}F\) or \(C\hat{G}F\) and \(C\hat{G}H\) Angles on a straight line should sum to 180	E1	dependent on the first mark; other forms of reasoning may be possible but the argument made must be complete and correct for the angles they have found. Allow e.g. ‘No angles are corresponding’ or ‘They are not corresponding’ or ‘Corresponding angles are (not) equal’ Allow e.g. ‘Opposite angles are equal.’ Allow e.g. ‘Alt angles are the same.’ Must be correct form of reasoning, do not allow F or Z angles or alternative angles

Scheme	Marks	Comments
(i) Complete correct method to find \(x\), e.g. 146 – 112 (alternate angles are equal) OR (\(QPR\) =) 180 – 146 (= 34) (angles on a straight line) and (\(QRP\) =) 180 – 112 – 34 (= 34) (angles in a triangle)	M1	Angles may be marked on the diagram FT ‘their 34’ for the second angle M0 for use of 180 – 112 = 68, 68 ÷ 2 = 34
34° (alternate angles are equal)	A1	CAO; 34° only is M0 A0
An appropriate reason linked to an angle	E1	(one reason only is sufficient for this mark)
(ii) Correct name and reason	B1	FT ‘their (i)’; answer must be consistent with their values from part (i) EXCEPT allow a restart with correct calculations to show equal base angles If (i) correct ‘Isosceles’ and equal base angles or two equal angles oe stated or shown; may be seen in (i) e.g. on the diagram If (i) incorrect ‘Scalene’ and no equal angles oe stated or shown; may be seen in (i) e.g. on the diagram Reason referencing sides only is not sufficient; condone poor spelling if intention is clear
	(6)

Scheme	Marks	Comments
(i) \(y\) = 180 – 146 (allied angles) and 180 – 112 – 34 (angles on a straight line)	M1	Angles may be marked on the diagram FT ‘their 34’ M0 for use of 180 – 112 = 68, 68 ÷ 2 = 34
34°	A1	CAO; 34° only is M0 A0
An appropriate reason linked to an angle	E1	(one reason only is sufficient for this mark) Allow ‘interior angles’ or ‘co-interior angles’