ABCD is a cyclic trapezium in which AD || BC. If ∠ABC

Home » Aptitude » Plane Geometry » Question

ABCD is a cyclic trapezium in which AD || BC. If ∠ABC = 70°, then ∠BCD is

1. 110°
2. 80°
3. 70°
4. 90 °

Correct Option: C

As per the given in question , we draw a figure cyclic trapezium ABCD

As we know that the sum of the opposite angles of a concyclic quadrilateral is 180°.
∴ ∠ABC + ∠ADC = 180°
⇒ 70° + ∠ADC = 180°
⇒ ∠ADC = 180° – 70° = 110°
∵ AD || BC
∴ ∠ADC + ∠BCD = 180°
⇒ 110° + ∠BCD = 180°
⇒ ∠BCD = 180° – 110° = 70°.