In the figure,if PQR is the tangent to a circ | vedclass

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Question

(A) Given that $AB \parallel PR$ and $PQR$ is a tangent at $Q$.By the alternate segment theorem,the angle between the tangent $QR$ and the chord $BQ$

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(A) Given that $AB \parallel PR$ and $PQR$ is a tangent at $Q$.By the alternate segment theorem,the angle between the tangent $QR$ and the chord $BQ$ is equal to the angle subtended by the chord in the alternate segment.Therefore,$\angle BAQ = \angle BQR = 70^{\circ}$.Since $AB \parallel PR$,the alternate interior angles are equal.Thus,$\angle ABQ = \angle BQR = 70^{\circ}$.In $	riangle ABQ$,the sum of angles is $180^{\circ}$.$\angle AQB + \angle ABQ + \angle BAQ = 180^{\circ}$.$\angle AQB + 70^{\circ} + 70^{\circ} = 180^{\circ}$.$\angle AQB + 140^{\circ} = 180^{\circ}$.$\angle AQB = 180^{\circ} - 140^{\circ} = 40^{\circ}$.

In the figure,if $PQR$ is the tangent to a circle at $Q$ whose center is $O$,$AB$ is a chord parallel to $PR$,and $\angle BQR = 70^{\circ}$,then $\angle AQB$ is equal to: (in $^{\circ}$)

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