Question 8a

ABCD is a parallelogram and PQRS is a rhombus. Find ∠x. (2 marks)

$Question 8a diagram$

Answer: 85 °

Workings

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∠ x = 180 - ∠ ROC (green)

∠ ROC (green) → 180 - 35 - ∠ OCR (blue)

∠ OCR (blue) → ∠ SCR (orange) - 60

since SCR is part of parallelogram ABCD

∠ SCR (orange) → 180 - 70 = 110 (adjacent angles)

∠ OCR (blue) → ∠ SCR (orange) - 60 = 110 - 60 = 50

∠ ROC (green) → 180 - 35 - ∠ OCR (blue) = 180 - 35 - 50 = 95

∠ x = 180 - ∠ ROC (green) = 180 - 95 = 85°

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