PQRS is a cyclic quadrilateral whose diagonals PR and QS intersect at the point T. SQR measures 72^, and QPR measures 28^. What is the measure of QRS? Option 1: 80^ Option 2: 100^ Option 3: 82^ Option 4: 60^

Answer: 80^. Solution: Since PQRS is a cyclic quadrilateral, SQR = SPR = 72^ SPQ = 72^ + 28^ = 100^. Hence, QRS = 180^ -100^ = 80^.

Geometry

Quadrilaterals

Easy

PQRS is a cyclic quadrilateral whose diagonals PR and QS intersect at the point T. $\angle SQR$ measures $72^\circ$ , and $\angle QPR$ measures $28^\circ$ . What is the measure of $\angle QRS$ ?

$80^\circ$

$100^\circ$

$82^\circ$

$60^\circ$

✅ Correct Option: 1

Since PQRS is a cyclic quadrilateral, $\angle SQR = \angle SPR = 72^\circ \Rightarrow \angle SPQ = 72^\circ + 28^\circ = 100^\circ$ . Hence, $\angle QRS = 180^\circ -100^\circ = 80^\circ$ .

BBA-DBE Bangalore 2025

The perimeter of a rhombus is $148 \text{ cm}$ and one of its diagonals is $70 \text{ cm}$ . Its area is equal to the area of a trapezium whose parallel sides are $x \text{ cm}$ and $50 \text{ cm}$ and the distance between the parallel sides is $14 \text{ cm}$ . What is the value of $x$ ?

PQRS is a cyclic quadrilateral whose diagonals PR and QS intersect at the point T. ∠SQR\angle SQR∠SQR measures 72∘72^\circ72∘, and ∠QPR\angle QPR∠QPR measures 28∘28^\circ28∘. What is the measure of ∠QRS\angle QRS∠QRS?

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BBA-DBE Bangalore Past Year Questions (Topic-Wise)

PQRS is a cyclic quadrilateral whose diagonals PR and QS intersect at the point T. $\angle SQR$ measures $72^\circ$ , and $\angle QPR$ measures $28^\circ$ . What is the measure of $\angle QRS$ ?