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Question
In the following figure,
- if ∠BAD = 96°, find ∠BCD and ∠BFE.
- Prove that AD is parallel to FE.
Solution
i. ABCD is a cyclic quadrilateral
∴ ∠BAD + ∠BCD = 180°
(Pair of opposite angles in a cyclic quadrilateral are supplementary)
`=>` ∠BCD = 180° – 96° = 84°
∴ ∠BCE = 180° – 84° = 96°
Similarly, BCEF is a cyclic quadrilateral
∴ ∠BCE + ∠BFE = 180°
(Pair of opposite angles in a cyclic quadrilateral are supplementary)
∴ ∠BFE = 180° – 96° = 84°
ii. Now, ∠BAD + ∠BFE
= 96° + 84°
= 180°
But these two are interior angles on the same side of a pair of lines AD and FE
∴ AD || FE
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