PQRS is a cyclic quadrilateral whose diagonals intersect at A- If - SQR - 80- and - QPR - 30- then find - SRQ- 70-60-80-50-

The correct option is A 70^∘Given, ∠ SQR = 80^∘. Since angles in the same segment are equal, we have ∠ SQR = ∠ SPR=80^∘. But, ∠ SPQ = ∠ SPR + ∠ RPQ = 80^∘ + 3 ...

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Byju's Answer

Standard IX

Mathematics

Theorem 5: Arcs That Subtend Equal Angle at Center Are Equal

PQRS is a cyc...

Question

PQRS is a cyclic quadrilateral whose diagonals intersect at A. If $∠ S Q R = 80^{\circ}$ and $∠ Q P R = 30^{\circ},$ then find $∠ S R Q .$

70^{\circ}

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60^{\circ}

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80^{\circ}

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50^{\circ}

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Solution

The correct option is A $70^{\circ}$
Given, $∠ S Q R = 80^{\circ} .$
Since angles in the same segment are equal, we have
$∠ S Q R = ∠ S P R = 80^{\circ} .$

But, $∠ S P Q = ∠ S P R + ∠ R P Q = 80^{\circ} + 30^{\circ}$
$⟹ ∠ S P Q = 110^{\circ}$
Since opposite angles are supplementary in a cyclic quadrilateral, we have
$∠ S P Q + ∠ S R Q = 180^{\circ} .$
$⟹ ∠ S R Q = 180^{\circ} - ∠ S P Q = 180^{\circ} - 110^{\circ} = 70^{\circ}$

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PQRS is a cyclic quadrilateral whose diagonals intersect at A. If ∠SQR=80∘ and ∠QPR=30∘, then find ∠SRQ.

PQRS is a cyclic quadrilateral whose diagonals intersect at A. If $∠ S Q R = 80^{\circ}$ and $∠ Q P R = 30^{\circ},$ then find $∠ S R Q .$