0580/12 Oct/Nov 2025, Question 14: Angles in a Triangle
Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Non-calculator · 3 marks
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The question, in short
Triangle DEF has vertices on the sides of triangle ABC, with angles 100°, 50°, 30° at A, B, C and 25°, 45°, 35° at D, F, E; find x, the angle at E in DEF.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 3 marks
- 1Angle BDF = 180 − 50 − 45 = 85° (triangle BDF)
- 2Angle FDE = 180 − 25 − 85 = 70° (angles on straight line AB)
- 3Angle DFE = 180 − 45 − 35 = 100° (angles on straight line BC)
- 4x = 180 − 70 − 100 = 10
Answer10
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