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In the given figure, O is the centre of the circle and ∠DAB = 50°. Calculate the values of x and y.

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It is given that O is the centre of the circle and ∠DAB = 50o

We know that the radii of the circle are equal

OA = OB

From the figure we know that

∠OBA = ∠OAB = 50o

Consider △ OAB

Using the angle sum property

∠OAB + ∠OBA + ∠AOB = 180o

By substituting the values

50o + 50o + ∠AOB = 180o

On further calculation

∠AOB = 180o – 50o – 50o

By subtraction

∠AOB = 180o – 100o

So we get

∠AOB = 80o

From the figure we know that AOD is a straight line

It can be written as

x = 180o – ∠AOB

By substituting the values

x = 180o – 80o

By subtraction

x = 100o

We know that the opposite angles of a cyclic quadrilateral are supplementary

So we get

∠DAB + ∠BCD = 180o

By substituting the values

50o + ∠BCD = 180o

On further calculation

∠BCD = 180o – 50o

By subtraction

y = ∠BCD = 130o

Therefore, the value of x is 100o and y is 130o.

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