4MA1/1FR Jun 2023, Question 10: Multi-Step Angle Reasoning
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1FR (Foundation) · Calculator · 5 marks
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The question, in short
Quadrilateral ABCD with straight lines ECD, BCF and GAD; angles ABC = 135°, ECF = 108°, ADC = 54°, GAB = x°. Find x, justifying each stage.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1BCF and ECD are straight lines crossing at C
- 2Angle BCD = 108° (vertically opposite angles are equal)
- 3The angles in quadrilateral ABCD add up to 360°
- 4Angle BAD = 360 − (108 + 135 + 54)
- 5Angle BAD = 360 − 297 = 63°
- 6GAD is a straight line, so x = 180 − 63 (angles on a straight line add up to 180°)
- 7x = 117
Answer117
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