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Choose the correct answer:

In the figure given 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: 65∘
We know that,

∠ Q R P = ∠ O Q P = 90 ∘

as the line joining the centre of the circle and the point where tangent meets the circle is 90 degree.
Now,

O R P Q

is quadrilateral and the sum of angles is 360.

∠ Q P R + ∠ Q O R + ∠ O Q R + ∠ O R P = 360 ∘ 50 ∘ + ∠ Q O R + 90 ∘ + 90 ∘ = 360 ∘ ​ ∠ Q O R = 360 − 230 = 130 ∘ ​

As we know that the Angle subtended by an arc at the centre of the circle is twice the angle subtended at the circumference

∠ Q S R = ∠ Q O R 2 ∠ Q S R = 1302 ∠ Q S R = 65 °

So, the correct answer is Option 1.

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