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Answer :
In quadrilateral PQRS, where PQ=PS and RQ=RS, triangle PQR and triangle PSR are both isosceles triangles. The base angles of these triangles are equal, which leads to angle PQR being equal to angle PSR.
In the given quadrilateral PQRS, we have PQ=PS and RQ=RS. This implies that triangle PQR and triangle PSR are both isosceles triangles.
Remember that in an isosceles triangle, the base angles are equal. Hence, in triangle PQR, angles PQR and PRQ are equal. Similarly, in triangle PSR, angles PSR and PRS are equal.
But since PRQ and PRS are the same angle PR in quadrilateral PQRS, it is also equal to itself, hence angle PQR = angle PSR.
Learn more about the topic of Isosceles Triangles here:
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