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Question
In the figure, given below, find:
- ∠BCD,
- ∠ADC,
- ∠ABC.
Show steps of your working.
Solution
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°
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