In the given figure, AB ∥ DC and ∠BAD = 100°. Calculate :

(i) ∠BCD

(ii) ∠ADC

(iii) ∠ABC.

(i) We know that:

Sum of opposite angles of a cyclic quadrilateral is 180°.

⇒ ∠BAD + ∠BCD = 180°

⇒ ∠BCD = 180° - 100°

⇒ ∠BCD = 80°.

Hence, ∠BCD = 80°.

(ii) Since AB ∥ DC, the angles ∠BAD and ∠ADC are consecutive interior angles along the transversal AD.

Therefore,

⇒ ∠BAD + ∠ADC = 180°

⇒ 100° + ∠ADC = 180°

⇒ ∠ADC = 180° - 100°

⇒ ∠ADC = 80°.

Hence, ∠ADC = 80°.

(iii) We know that:

Sum of opposite angles of a cyclic quadrilateral is 180°.

⇒ ∠ABC + ∠ADC = 180°

⇒ ∠ABC + 80° = 180°

⇒ ∠ABC = 180° - 80°

⇒ ∠ABC = 100°.

Hence, ∠ABC = 100°.