Question : In a triangle $PQR$, $QR$ is produced to $S$. If $\angle PRS=(9x-15^{\circ}), \angle RPQ=2x$ and $\angle PQR = (4{x}+15^{\circ})$, what is the value of $x$?
Option 1: 55
Option 2: 20
Option 3: 10
Option 4: 75
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Correct Answer: 10
Solution :
Given: $\angle PRS=(9x-15^{\circ}), \angle RPQ=2x$ and $\angle PQR=(4{x}+15^{\circ})$
Applying exterior angle property, we get:
$\angle PRS=\angle RPQ+\angle PQR$
⇒ $(9x-15^{\circ}) = 2x+(4{x}+15^{\circ})$
⇒ $3x=30^{\circ}$
⇒ $x=10^{\circ}$
Hence, the correct answer is 10.
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