Question

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

Answer 1

The value of ∠PQR = 81° and ∠PQS = 99°.

Step-by-step explanation:

It is given that,

∠PQR and ∠PQS are linear pair of angles

i.e., ∠PQR + ∠PQS = 180° ...... (i)

Also given,

11 × ∠PQR = 9 × ∠PQS

⇒ ∠PQR = $\frac{9}{11}$ × ∠PQS ..... (ii)

Now,

By substituting (ii) in (i), we get

[$\frac{9}{11}$ × ∠PQS] + ∠PQS = 180°

⇒ ∠PQS [$\frac{9}{11}$ + 1] = 180°

⇒ ∠PQS [$\frac{9+11}{11}$] = 180°

⇒ ∠PQS [$\frac{20}{11}$] = 180°

⇒ ∠PQS = 180° × [$\frac{11}{20}$]

⇒ ∠PQS = 9 × 11

⇒ ∠PQS = 99°

By substituting the value of ∠pqs in (ii), we get

∠PQR = $\frac{9}{11}$ × ∠PQS

⇒ ∠PQR = $\frac{9}{11}$ × 99°

⇒ ∠PQR = 9 × 9

⇒ ∠PQR = 81°

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