Question

AB is parallel to DC. AD is parallel to BC.∠ CDB = 72°.∠ CAB = 31°.Work out x, explaining each stage of your working in the comment box.

Answer 1

AB is parallel to CD and BD is transversal,

∠D = ∠B [alt. int. ∠s]

∴∠B = 72°

AB is parallel to CD and CA is transversal

∠A = ∠C [alt. int. ∠s]

∴∠C = 31°

Putting centre point as O,

In ΔAOB

∠A + ∠B + ∠O = 180° [ASP of Δs]

31 + 72 + ∠O = 180

∠O = 180 - 103

∠O = 77°

∠x and ∠O form linear pair

∴∠x + ∠O = 180°

∠x = 180 - 77

∠x = 103°

∴ x = 103°

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