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Choose the correct answer:

In the given figure below, ∠QSR is equal to

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65∘

50∘

70∘

75∘

answer is A.

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Detailed Solution

The correct answer is option 1.
angle between the radius and tangent to the circle is equal to

90 °

Therefore,

∠ O Q P = ∠ O R P = 90 °

In quadrilateral OQPR,

∠ O Q P = ∠ O R P = 90 ° ∠ Q P R = 50 °

Using angle sum property:

∠ O Q P + ∠ O R P + ∠ Q P R + ∠ Q O R = 360 ° ⇒ 90 ∘ + 90 ∘ + 50 ∘ + ∠ Q O R = 360 ° ⇒ 230 ° + ∠ Q O R = 360 ° ⇒ ∠ Q O R = 130 °

Using the property: the angle made by an arc at the center is equal to two times the angle made by the same arc at the circumference of the circle.

b ⇒ ∠ Q O R = 2 ∠ Q S R ⇒ 130 ∘ = 2 ∠ Q S R ⇒ 130 ° 2 = 2 ∠ Q S R 2 ⇒ ∠ Q S R = 65 °

The answer is option 1.

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