Question

In the given figure, ABCD is a cyclic quadrilateral in which AB || DC.
If ∠BAD = 100°, find
(i) ∠BCD (ii) ∠ADC (iii) ∠ABC.

Answer 1

In cyclic quadrilateral ABCD, AB is parallel to DC and ∠BAD = ∠100°.
(i)
∠BCD + ∠BAD = 180° (ABCD is a cyclic quadrilateral )
⇒∠BCD + 100° = 180°
⇒∠BCD = 180° – 100° = 80°
∴ ∠BCD = 80°

(ii)
∠ADC +∠BAD = 180° (Interior angles on the same side of transversal are supplementary)
∠ADC + 100° = 180°
∴ ∠ADC = 80°

(iii)
∠ABC + ∠BCD = 180° (Interior angles on the same side of transversal are supplementary)
∴ ∠ABC = 180°- 80° = 100°