Angles (Including Parallel Lines): Eduqas GCSE Foundation June 2018 Paper 1 Q17

Foundation June 2018 Paper 1 Q17

EduqasFoundationCurrent spec4 marksAngles (Including Parallel Lines)

17. In the diagram, ABC is a triangle.
BC is parallel to DEF.
AEB and AFC are straight lines.

Diagram not drawn to scale

Show that \(x = 33^\circ\).
You must give a reason for each step of your working. [4]

Mark scheme

Scheme	Marks	Comments
		Answers may be seen on the diagram; it must be clear from description or reasoning which angles are being calculated or used *Alternative method for first 2 marks:*
Angle AEF or Angle DEB = 93° (Angles on a straight line (sum to 180))	B1	Angle BEF = 87° (Vertically opposite angles (are equal))
Angle AFE = 54° (Corresponding angles (are equal)) or Angle ABC = 93° (Corresponding angles (are equal) or alternate angles (are equal))	B1	Angle ABC = 93° (Interior angles (sum to 180))
(\(x\) = ) 180° – 93° – 54° = 33° (Angles in a triangle (sum to 180))	B1	or equivalent e.g. 93 + 33 + 54 = 180
A correct reason linked to a correct statement	B1
	(4)

Alternative method 1: Assuming \(x = 33^\circ\):

Scheme	Marks	Comments
Angle ABC = 180° – 33° – 54° = 93° (Angles in a triangle (sum to 180))	B1
Angle AEF or Angle DEB = 93° (Angles on a straight line (sum to 180))	B1
Angle ABC = Angle AEF (Corresponding angles (are equal)) or Angle ABC = Angle DEB or (Alternate angles (are equal))	B1
A correct reason linked to a correct statement	B1

Alternative method 2: Assuming \(x = 33^\circ\):

Scheme	Marks	Comments
Angle AFE = 54° (Corresponding angles (are equal))	B1
Angle AEF = 180° – 33° – 54° = 93° (Angles in a triangle (sum to 180))	B1
93 + 87 = 180 (Angles on a straight line (sum to 180))	B1
A correct reason linked to a correct statement	B1

Alternative method 3:

Scheme	Marks	Comments
Angle AFE = 54° (Corresponding angles (are equal))	B1
\(x + 54 = 87\) (Exterior angle (is equal to the sum of the two opposite interior angles))	B1
\(x = 87 - 54 = 33\)	B1
A correct reason linked to a correct statement	B1