Question

Step by step explanation...

Don't copy❌....

Cbse class 10th....​

Answer 1

Answer:

Step-by-step explanation:

PQ = PR

Since tangents drawn from an external point to a circle are equal.

And PQR is an isosceles triangle

thus, ∠RQP = ∠QRP

∠RQP + ∠QRP + ∠RPQ = 180° [Angle sum property of a triangle]

2∠RQP + 30° = 180°

2∠RQP = 150°

∠RQP = ∠QRP = 75°

∠RQP = ∠RSQ = 75°  [ Angles in alternate Segment Theorem states that angle between chord and tangent is  equal to the angle in the alternate segment]

RS is parallel to PQ

Therefore ∠RQP = ∠SRQ = 75°    [Alternate angles]

∠RSQ = ∠SRQ = 75°

Therefore QRS is also an isosceles triangle

∠RSQ + ∠SRQ + ∠RQS = 180°  [Angle sum property of a triangle]

75° + 75° + ∠RQS = 180°

150° + ∠RQS = 180°

∠RQS = 30°

Answer 2

Answer:

Step-by-step explanation:

Since tangents drawn from an external point to a circle are equal.

So, PQ = PR, and PQR is an isosceles triangle.

So, ∠RQP = ∠QRP

Again, ∠RQP + ∠QRP + ∠RPQ = 180

=> 2∠RQP + 30 = 180

=> 2∠RQP = 180 - 30

=> 2∠RQP = 150

=> ∠RQP = 150/2

=> ∠RQP = 75

=> ∠RQP = ∠QRP = 75

and ∠RQP = ∠RSQ = 75

=> ∠RQP = ∠SRQ = 75 {alternalte angles}

So, QRS is an isosceles triangle. {Since sides opposite to equal angles of a triangle are equal.}

Now, ∠RSQ + ∠SRQ + ∠RQS = 180° {Angle sum property of a triangle}

=> 75 + 75 + ∠RQS = 180

=> 150 + ∠RQS = 180

=> ∠RQS = 180 - 150

=> ∠RQS = 30°

Mark as brainliest please