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

Question

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

Team Careers360 · Accepted Answer

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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Question : PQRS is a cyclic quadrilateral. In PQRS,∠P is opposite to ∠R. If ∠P and ∠R are 3x+5 and 4x respectively, then what is the value of x ?Option 1: 28 degreesOption 2: 35 degreesOption 3: 25 degreesOption 4: 30 degrees

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Question : $PQRS$ is a cyclic quadrilateral. In $PQRS, ∠ P$ is opposite to $∠ R$ . If $∠ P$ and $∠ R$ are $3 x + 5$ and $4 x$ respectively, then what is the value of $x$ ?
Option 1: 28 degrees
Option 2: 35 degrees
Option 3: 25 degrees
Option 4: 30 degrees