Question

In the figure, given below, find:

1. ∠BCD,
2. ∠ADC,
3. ∠ABC.

Show steps of your working.

Answer 1

i. ∠BCD + ∠BAD = 180°

(Sum of opposite angles of a cyclic quadrilateral is 180°)

`=>` ∠BCD = 180° – 105° = 75°

ii. Now, AB || CD

∴ ∠BAD + ∠ADC = 180°

(Interior angles on the same side of parallel lines is 180°)

`=>` ∠ADC = 180° – 105° = 75°

iii. ∠ADC + ∠ABC = 180°

(Sum of opposite angles of a cyclic quadrilateral is 180°)

`=>` ∠ABC = 180° – 75° = 105°