Mathematics
In the following figure,
(i) if ∠BAD = 96°, find ∠BCD and ∠BFE.
(ii) Prove that AD is parallel to FE.
Circles
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Answer
(i) ABCD is a cyclic quadrilateral.
So, ∠BAD + ∠BCD = 180° [As sum of opposite angles in a cyclic quadrilateral = 180°]
⇒ ∠BCD = 180° - ∠BAD
= 180° - 96°
= 84°.
As DCE is a straight line.
∴ ∠BCE = 180° - ∠BCD
= 180° - 84° = 96°.
BCEF is a cyclic quadrilateral,
So, ∠BCE + ∠BFE = 180°
⇒ ∠BFE = 180° - ∠BCE
= 180° - 96°
= 84°.
Hence, ∠BCD = 84° and ∠BFE = 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.
Hence, proved that AD || FE.
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