Question

PQRS is a cyclic quadrilateral such that side PQ is the diameter of the circle and anglePSR = 115°. The value of angleOPR is​

Answer 1

Given : PQRS is a cyclic quadrilateral such that side PQ is the diameter of the circle  .  ∠PSR = 115°.

To Find :  ∠OPR

Solution:

PQRS is a cyclic quadrilateral

Sum of opposite angles in   cyclic quadrilateral = 180°

∠PSR  + ∠PQR = 180°

∠PSR = 115°  

=> 115°   + ∠PQR = 180°

=> ∠PQR =65°

PQ is Diameter

∠PRQ = 90°

in  ΔPQR

∠PRQ + ∠PQR + ∠QPR = 180°

=> 90° + 65° +  ∠QPR = 180°

=> ∠QPR = 25°

PQ is Diameter hence O lies on PQ

=> ∠OPR  = ∠QPR

=> ∠OPR  = 25°

Learn More:

In a cyclic quadrilateral ABCD, if ∠A and ∠C are in the ratio 3 : 2 ...

https://brainly.in/question/30112097

in the figure ABCD is a cyclic quadrilateral the tangents at the points ...

https://brainly.in/question/13340209

IN A CYCLIC QUADRILATERAL ABCD ANGLE A AND C ARE IN ...

https://brainly.in/question/30426896