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In the following figure, (i) if ∠BAD = 96degree, find ∠BCD and ∠BFE. (ii) Prove that AD is parallel to FE.

Selina Solutions Concise Class 10 Maths Chapter 17 ex. 17(A) - 26

Solution:

\[ABCD\]is a cyclic quadrilateral

(i) Hence, \[\angle BAD\text{ }+\angle BCD\text{ }=\text{ }{{180}^{o}}\]

[Pair of opposite angles in a cyclic quadrilateral are supplementary]

\[\angle BCD\text{ }=\text{ }{{180}^{o}}-\text{ }{{96}^{o}}~=\text{ }{{84}^{o}}\]

And, \[\angle BCE\text{ }=\text{ }{{180}^{o}}-\text{ }{{84}^{o}}~=\text{ }{{96}^{o}}~\][Linear pair of angles]

(ii) Similarly, \[BCEF\]is a cyclic quadrilateral

So, \[\angle BCE\text{ }+\angle BFE\text{ }=\text{ }{{180}^{o}}\]

[Pair of opposite angles in a cyclic quadrilateral are supplementary]

\[\angle BFE\text{ }=\text{ }{{180}^{o}}-\text{ }{{96}^{o~}}=\text{ }{{84}^{o}}\]