Question : $\mathrm{PQRS}$ is a cyclic quadrilateral. In $\mathrm{PQRS}, \angle \mathrm{P}$ is opposite to $\angle \mathrm{R}$. If $\angle \mathrm{P}$ and $\angle \mathrm{R}$ are $3 \mathrm{x}+5$ and $4 \mathrm{x}$ respectively, then what is the value of $\mathrm{x}$ ?
Option 1: 28 degrees
Option 2: 35 degrees
Option 3: 25 degrees
Option 4: 30 degrees
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Correct Answer: 25 degrees
Solution : Given, $\angle \mathrm{P}=3\mathrm{x}+5$ and $\angle \mathrm{R}=4\mathrm{x}$ Since $\angle \mathrm{P}$ and $\angle \mathrm{R}$ are opposite to each other in a cyclic quadrilateral, we have $\angle \mathrm{P}+\angle \mathrm{R}=180^\circ$ ⇒ $3\mathrm{x}+5+4\mathrm{x}=180^\circ$ ⇒ $\mathrm{x}=25^\circ$ Hence, the correct answer is 25 degrees.
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