Question 7

ABC is an isosceles triangle. AB = AC. AFB, CEB and FED are straight lines. Find ∠BDF. (4 marks)

$Question 7 diagram$

Answer: 18 °

Workings

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∠BDF = 180 - ∠ EFB (green) - ∠ FBD (blue)

∠ EFB (green) → 180 - 123 = 57 (angle on straight line)

∠ FBD (blue) → ∠ FBE (orange) + 46

∠ FBE (orange) part of isosceles ▵ ABC

∠ FBE (orange) → (180 - 62) ÷ 2 = 59

∠ FBD (blue) → ∠ FBE (orange) + 46 = 59 + 46 = 105

∠BDF = 180 - ∠ EFB (green) - ∠ FBD (blue) = 180 - 57 - 105 = 18 °

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