In the given figure: ( v ); prove that x = angle BAD + angle ABC + angle BCD
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Construction :-
Join B to D and extend BD to E.
Now,
in ΔABD,
α + ∠ABD = ∠ADE (i) [ exterior angle ]
Similarly,
In ΔBCD,
∠DBC + = ∠CDE (ii)
Add (i) and (ii)
⇒ ∠ADE + ∠CDE = (∠ABD + ∠DBC) + α +
⇒ x = β + α +
[ as ∠ADE + ∠CDE = x, ∠ABD + ∠DBC = β ]
Hence
Proved
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priya1431434:
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