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(C) Since $\angle PQR$ and $\angle PQS$ form a linear pair,their sum is $180^{\circ}$.$\angle PQR + \angle PQS = 180^{\circ}$ (Equation $1$).Given tha

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$81^{\circ}$ and $99^{\circ}$

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(C) Since $\angle PQR$ and $\angle PQS$ form a linear pair,their sum is $180^{\circ}$.$\angle PQR + \angle PQS = 180^{\circ}$ (Equation $1$).Given that $11 \angle PQR = 9 \angle PQS$,we can write $\angle PQS = \frac{11}{9} \angle PQR$.Substitute this into Equation $1$:$\angle PQR + \frac{11}{9} \angle PQR = 180^{\circ}$.$\frac{9 \angle PQR + 11 \angle PQR}{9} = 180^{\circ}$.$\frac{20 \angle PQR}{9} = 180^{\circ}$.$20 \angle PQR = 1620^{\circ}$.$\angle PQR = \frac{1620^{\circ}}{20} = 81^{\circ}$.Now,find $\angle PQS$:$\angle PQS = 180^{\circ} - 81^{\circ} = 99^{\circ}$.Thus,$\angle PQR = 81^{\circ}$ and $\angle PQS = 99^{\circ}$.

$\angle PQR$ and $\angle PQS$ are a linear pair of angles. If $11 \angle PQR = 9 \angle PQS$,then find $\angle PQR$ and $\angle PQS$.

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