Mathematics
In the adjoining figure, PQR is a tangent at Q to a circle. If AB is a chord parallel to PR and ∠BQR = 70°, then ∠AQB is equal to
20°
40°
35°
45°
Circles
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Answer
From figure,
BQ is chord and PQR is a tangent.
∠BQR = ∠A (∵ angles in alternate segment are equal.)
As AB || PQR
∠BQR = ∠B (∵ alternate angles are equal)
∴ ∠A = ∠B = 70°
We know that sum of angles in a triangle = 180°.
In △AQB,
⇒ ∠A + ∠B + ∠AQB = 180°
⇒ 70° + 70° + ∠AQB = 180°
⇒ 140° + ∠AQB = 180°
⇒ ∠AQB = 180° - 140°
⇒ ∠AQB = 40°.
Hence, Option 2 is the correct option.
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