Question 36

ABCD is a cyclic trapezium with AD || BC . If ∠A = 105° , then other three angles are

Solution

ABCD is a cyclic trapezium and AD || BC

Sum of angles on the same side of transversal = 180°

=> ∠A + ∠B = 180°

=> ∠B = 180° - 105° = 75°

Also, sum of opposite angles of a cyclic quadrilateral = 180°

=> ∠A + ∠C = 180°

=> ∠C = 180° - 105° = 75°

Similarly, ∠B + ∠D = 180°

=> ∠D = 180° - 75° = 105°

=> Ans - (A)

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