Question

In the given circle with centre 0, (x + y) equals

Answer 1

Answer:

140°

Step-by-step explanation:

x+y equals 140° because it is horz

Answer 2

Answer:

In Circle with centre 0, (x + y) equals 220.

Step-by-step explanation:

Triangle OPS is an isosceles triangle,  

side OP = side OS and

∠OPS = ∠OSP

given ∠OPS = 40°

∴ ∠OSP = 40

From ΔPOS,

∠POS + ∠OPS + ∠OSP = 180

∠POS = 180 - ( ∠OPS + ∠OSP )

∠POS = 180 - (40 +40) (from above)

∠POS = 180 - 80

∠POS = 100

since from the figure PQ is the diameter of the circle,

∠POS + ∠QOS = 180

100 + y = 180 ( here ∠POS = 100 and  given ∠QOS = y)  

y = 180 - 100

y = 80

we know that the opposite angles of a cyclic quadrilateral are

supplementary.

∠QPS + ∠QRS = 180

40 + x = 180

x = 180 - 40

x = 140

therefore x+y = 140 + 80

x + y = 220.

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