Question

In fig. o is the centre of a circle , prove that angle x + angle y = angle z.

Answer 1

∠EBF = 1/2∠EOF = 1/2∠z [∵ Angle subtended by an arc of a circle at the centre in twice the angle subtended by it at any point of the remaining part of the circle]

[∵ Angle subtend by any arc of a circle at the centre is twice the angle subtended by it at any point of the remaining part of the circle]

In quadrilateral ABCD ∠ABC + ∠BCD + ∠CDA + ∠BAD = 2 × 1800

[ Angle Sum Property of a quadrilateral]

=> 1800 - 1/2∠z + ∠y + 1800 - 1/2∠z + ∠x = 2 × 1800

=> ∠x + ∠y = ∠z

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