Question

Tangents PQ and PR are drawn from an external point P to a circle with centre O, such that angle RPQ=30°. A chord RS is drawn parallel to the tangent PQ. Find angle RQS.


Answer is 30° but solve karke btao jaldi please....

${\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{Don't....Spam}}}}}}}}}}}}}}}}}}}}}}}}}}​​​​​​​​​​​​​​​​​​​$​

Answer 1

Given Parameters :

• ∠RPQ = 30°

• RS ∥ PQ

Unknown :

• ∠RQS = ?

Answer:

→ RS ∥ PQ (Given)

→ PR = PQ (By theorem 10.2)

→ ∠R = ∠Q (Opposite angles to equal sides are also equal)

Now,In ∆PQR

➝ ∠P + ∠Q + ∠R = 180° (Angle sum property)

➝ 30 + x + x = 180°

➝ 30 + 2x = 180

➝ 2x = 180 - 30

➝ 2x = 150

Dividing both sides by 2 we get :

➝ x = 75°

➝ SR ∥ PQ

➝ 75° = ∠SRQ = ∠PQR [Alternate angle]

➝ ∠QSR = ∠QRP = 75 [Alternate segment theorem]

Now, In ∆SQR

᠉ ∠RQS + 75 + 75 = 180

᠉ ∠RQS + 150 = 180

᠉ ∠RQS = 180 - 150

᠉ ∠RQS = 30°