Question

In the adjacent rectangle ABCD,∠OCD =30°. Calculate ∠BOC. What type of triangle is BOC?

Answer 1

ABCD is a rectangle

Diagonals AC and BD bisect each other at O and AC = BD.

AO = OC = BO = OD

OCD = ODC = 30°

On ΔCOD, ∠ODC + ∠OCD + ∠COD = 180˚

30° + 30° + ∠COD = 180°

60° + ∠COD = 180°

∴ ∠COD = 180˚ – 60˚ =120°

∠COD + ∠COB = 180˚

∠COB = 180˚ – 120˚

∠COB = 60°

∴ Δ BOC is an isosceles triangle

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Answer 2

ABCD is a rectangle

Diagonals AC and BD bisect each other at O and AC = BD.

AO = OC = BO = OD

OCD = ODC = 30°

On ΔCOD, ∠ODC + ∠OCD + ∠COD = 180˚

30° + 30° + ∠COD = 180°

60° + ∠COD = 180°

∴ ∠COD = 180˚ – 60˚ =120°

∠COD + ∠COB = 180˚

∠COB = 180˚ – 120˚

∠COB = 60°

∴ Δ BOC is an isosceles triangle