In the figure (ii) given below, ABCD is a cyclic trapezium in which AD is parallel to BC and ∠B = 70°, find

(i) ∠BAD

(ii) ∠BCD

(i) In trapezium sum of angles on same side = 180°.

⇒ ∠ABC + ∠BAD = 180°
⇒ 70° + ∠BAD = 180°
⇒ ∠BAD = 180° - 70°
⇒ ∠BAD = 110°

Hence, the value of ∠BAD = 110°.

(ii) ABCD is a cyclic quadrilateral as all vertices lie on the circumference of the circle.

Sum of opposite angles of cyclic quadrilateral = 180°

⇒ ∠BAD + ∠BCD = 180°
⇒ 110° + ∠BCD = 180°
⇒ ∠BCD = 180° - 110°
⇒ ∠BCD = 70°.

Hence, the value of ∠BCD = 70°.