Question : ABCD is a cyclic quadrilateral in which angle B is opposite to angle D. If $\angle \mathrm{B}=(\mathrm{x}+10)^{\circ}$ and $\angle \mathrm{D}=(2 \mathrm{x}+35)^{\circ}$, then what is the value of $\mathrm{x}$?
Option 1: 40$^{\circ}$
Option 2: 45$^{\circ}$
Option 3: 50$^{\circ}$
Option 4: 35$^{\circ}$
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Correct Answer: 45$^{\circ}$
Solution :
Given, ABCD is a cyclic quadrilateral in which angle B is opposite to angle D.
$\angle \mathrm{B}=(\mathrm{x}+10)^{\circ}$ and $\angle \mathrm{D}=(2 \mathrm{x}+35)^{\circ}$
We know the opposite angles of a cyclic quadrilateral are supplementary.
So, $\angle \mathrm{B}+\angle \mathrm{D}=180^\circ$
⇒ $\mathrm{x}+10^\circ+2 \mathrm{x}+35^\circ=180^\circ$
⇒ $3\mathrm{x}+45^\circ=180^\circ$
⇒ $3\mathrm{x}=135^\circ$
⇒ $\mathrm{x}=45^\circ$
Hence, the correct answer is 45$^{\circ}$.
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