Question
In a cyclic quadrilateral $ABCD$ if $\text{m}\angle\text{A}=\big(\text{m}\angle\text{C}\big).$ Find $\text{m}\angle\text{A}.$
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Answer
We have, $\angle\text{A}=3\angle\text{C}$
Let $\angle\text{C}=\text{x}$ Then, $\angle\text{A}=\text{3x}$
$\therefore\angle\text{A}+\angle\text{C}=180^\circ$ [Opposite angles of cyclic quad.]
$\Rightarrow\text{3x}+\text{x}=180^\circ$
$\Rightarrow\text{4x}=180^\circ$
$\Rightarrow\text{x}=\frac{180^\circ}{4}=45^\circ$
$\therefore\angle\text{A}=\text{3x}$
$=3\times45^\circ$
$=135^\circ$
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