Question

In a cyclic quadrilateral ABCD , AB || CD and ∠ B = 65° , find the remaining angles.

Answer 1

∠ B = 65°( given) 

∠ B + ∠ D = 180 (Opposite angles of a cydic quadrilateral) 

65 + ∠ D = 180 

∠ D = 115

Also, AB || CD 

∴  ∠ B + ∠ C = 180 (Sum of angles on same side of transversal) 

∠ C = 180 - 65 = 115 

Again, ∠ A+ ∠ C = 180° (Opposite angles of a cyclic quadrilateral

∠ A = 180 - 115  = 65°