Question

In a trapezium ABCD, side AB is parallel to side DC. If ∠A = 78° and ∠C = 120°, find angles B and D.

Answer 1

∵ AB || DC and BC is transversal

∴∠B and ∠C, ∠A and ∠D are Cointerior angles with their sum = 180°

i.e. ∠B + ∠C = 180°

⇒ ∠B + 120° = 180°

⇒ ∠B = 180° – 120°

⇒ ∠B = 60°

Also ∠A + ∠D = 180°

⇒ 78° + ∠D = 180°

⇒ ∠D = 180° – 78°

∠D = 102°