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In a trapezium ABCD, AB || CD and ∠BCD = 50°. If angle bisectors of ∠BCD and ∠ADC meet at point O and ∠COD = 115°, then what is the measure of ∠BAD?

In a trapezium ABCD, AB || CD and ∠BCD = 50°. If angle bisectors of ∠BCD and ∠ADC meet at point O and ∠COD = 115°, then what is the measure of ∠BAD? Correct Answer 100°

∠ABC = 180° – 50° = 130°

∠OCD = 50°/2 = 25°

Let ∠ODC = x

In ∆BOD

∠OCD + ∠ODC + ∠COD = 180°

25° + x + 115° = 180°

x = 40°

∠ADC = 2x = 80°

∠ADC = Exterior ∠A = 80°

∠BAD = 180° – 80°

∠BAD = 100°

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