4MA1/1F Jun 2019, Question 8: Multi-Step Angle Reasoning
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1F (Foundation) · Calculator · 5 marks
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The question, in short
Using the diagram with DC = DB, angle ABC = 90°, angle CDB = 116° and angle DAB = 55°, work out the angle marked x, justifying each stage.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1DC = DB, so triangle DBC is isosceles
- 2angle DBC = (180° − 116°) ÷ 2 = 32° (base angles of an isosceles triangle are equal)
- 3angle ABC = 90°, so angle ABD = 90° − 32° = 58°
- 4angle ADB = 180° − 58° − 55° = 67° (angles in a triangle add up to 180°)
- 5At D the angles 116°, 67° and x make a complete turn
- 6x = 360° − 116° − 67° = 177° (angles at a point add up to 360°)
Answer177
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