Foundation June 2021 Paper 2 Q19

EdexcelCurrent spec5 marksAngles (Including Parallel Lines)

Lines ABCD and FGHI are parallel, with arrows. Line EBGJ passes through B and G and continues to J below. Line ECH passes through C to H. BE and CE are marked equal. Angle BEC is 44 degrees. Angle JGH is marked below line FGHI, between GJ and GH

Diagram NOT accurately drawn

\(ABCD\) and \(FGHI\) are parallel straight lines.
\(EBGJ\) and \(ECH\) are straight lines.

\(BE = CE\)
Angle \(BEC\) = 44°

Work out the size of angle \(JGH\).
Give a reason for each stage of your working.

(5)

Mark scheme

Scheme	Marks
Angle \(EBC\) or \(ECB\) = (180 – 44) ÷ 2 (= 68)	M1
Angle \(GBC\) = 180 – “68” (= 112) or Angle \(GBC\) = “68” + 44 (= 112) or Angle \(BGH\) = “68” (same as \(EBC\)) Angle \(ABE\) = 180 – “68” (= 112) and Angle \(BGF\) = “112” or Angle \(ABG\) = “68” and Angle \(BGH\) = “68” or Angle \(FGJ\) = “68” or Angle \(BGF\) = 180 – “68” (= 112)	M1
Working not required, so correct angle scores 3 marks (unless from obvious incorrect working) Answer: 112	A1
NB: reasons must include the underlined words Accept ∠ for angle(s) and △ for triangle For all angles: They must be clearly stated as the correct angle or shown on the diagram in the correct position. (eg just seeing 68 in working without a label is not sufficient for the award of a mark for angle \(EBC\))	B2
	(5)
	(5 marks)

Notes

M1: Could be seen on diagram

M1: for a method to as far as one step away from working out Angle \(JGH\) (an angle corresponding or vertically opposite to \(JGH\) or at the same point on a straight line with \(JGH\))
Could be seen on diagram.
(the award of this mark also implies the previous M1)

A1: Could be seen in correct place on diagram

B2: for correct answer with full reasons for their method
eg isosceles triangle (or 2 equal sides, 2 equal angles)
Angles in a triangle sum to 180° or angles in a triangle
Angles on a straight line sum to 180°
Angles on a straight line sum to 180°
Exterior angle in a triangle is equal to the two opposite interior angles.
Vertically opposite angles are equal.
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal
Allied angles sum to 180° (or co-interior angles)
Angles at a point (or full turn) add up to 360° (or angles at a point)
(B1 for one correct reason appropriate to their method, dep on M1)