Question 10b

ABCD is a parallelogram. DG is a straight line. ∠ABC = 65°, ∠CAD = 50° and ∠CFG = 140°. Find ∠CDF. (3 marks)

$Question 10b diagram$

Answer: 25 °

Workings

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∠ CDF is part of triangle CDF

∠ CDF = 180 - ∠ FCD (green) - ∠ BFC (orange)

∠ BAD (green) → 180 - 65 = 115

opposite angles are the same in parallelogram

∠ FCD (green) = 115

∠ BFC (orange) → 180 - 140 = 40

∠ CDF = 180 - ∠ FCD (green) - ∠ BFC (orange) = 180 - 115 - 40 = 25

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