Question

in the figure PQRS is a cyclic quadrilateral.,O is the centre of the circle.If angle QOS =160°,find the measures of angle QRS and angle QMS.​

Answer 1

∠QRS  =  ∠QMS = 100°

Step-by-step explanation:

∠QOS = 160°

∠QOS = 2∠QPS  ( angle subtended by arc QS at center and circle)

=> 2∠QPS   = 160°

=> ∠QPS   = 80°

QRSP is a  cyclic quadrilateral

=> ∠QRS + ∠QPS = 180°  ( sum of oppsoite angle of cyclic quadrilateral)

=> ∠QRS + 80° = 180°

=> ∠QRS  = 100°

∠QRS = ∠QMS  ( angle subtended by same chord QS in same arc  segment)

=> ∠QMS = 100°

Learn more:

in given figure angle poq =100 and angle pqr=30,then find angle rpo ...

https://brainly.in/question/13203903

O is the centre of the circle and chord AC and BD intersect at P such ...

https://brainly.in/question/13936534

The vertices of a A PQR lie on a circle with centre O. SR is a tangent ...

https://brainly.in/question/13308847

Answer 2

Answer:

Step-by-step explanation: