In a cyclic quadrilateral PQRS,angle QPR = 40 | vedclass

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(B) In a cyclic quadrilateral $PQRS$,angles subtended by the same arc at the circumference are equal.Since $\angle QPR$ and $\angle QSR$ subtend the s

Vedclass · Accepted Answer

$70$

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(B) In a cyclic quadrilateral $PQRS$,angles subtended by the same arc at the circumference are equal.Since $\angle QPR$ and $\angle QSR$ subtend the same arc $QR$,we have $\angle QSR = \angle QPR = 40^{\circ}$.Given $\angle PSQ = 70^{\circ}$,the total angle $\angle PSR = \angle PSQ + \angle QSR = 70^{\circ} + 40^{\circ} = 110^{\circ}$.In a cyclic quadrilateral,the sum of opposite angles is $180^{\circ}$.Therefore,$\angle PQR + \angle PSR = 180^{\circ}$.$\angle PQR + 110^{\circ} = 180^{\circ}$.$\angle PQR = 180^{\circ} - 110^{\circ} = 70^{\circ}$.

In a cyclic quadrilateral $PQRS$,$\angle QPR = 40^{\circ}$ and $\angle PSQ = 70^{\circ}$,then find $\angle PQR$. (in $^{\circ}$)

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