Question

PQR and PQS are linear pair of angles. If
11 PQR = 9 PQS, then find PQR and PQS.​

Answer 1

Answer: PQR=99 PQS = 81

Step-by-step explanation: Let the angles be 11x and 9x respectively..

9x+11x= 180 degrees

20x=180°

x= 9°

Therefore, the angles are 11*9=99,9*9=81

Answer 2

The value of $\angle{PQR}=81^{\circ}$ and $\angle{PQS}=99^{\circ}$.

Explanation:

If ∠PQR and ∠PQS are linear pair , then

∠PQR + ∠PQS = 180°  .....(1)  [linear pair of angles must add up to 180 degrees.]

Also, 11 ∠PQR  = 9 ∠PQS

⇒  $\angle{PQR}=\dfrac{9}{11}(\angle{PQS})$ ..............(2)

Then, from (1) and (2) , we have

$\dfrac{9}{11}(\angle{PQS})+\angle{PQS}=180^{\circ}\\\\\Rightarrow\ \dfrac{9+11}{11}(\angle{PQS})=180^{\circ}\\\\\Rightarrow\ \dfrac{20}{11}(\angle{PQS})=180^{\circ}\\\\\Rightarrow \angle{PQS}=180^{\circ}\times \dfrac{11}{20}=9^{\circ}\times11=99^{\circ}$

From (2) , we have

$\angle{PQR}=\dfrac{9}{11}(99)=9\times9=81^{\circ}$

Hence, the value of $\angle{PQR}=81^{\circ}$ and $\angle{PQS}=99^{\circ}$.

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