In the adjoining figure, ABCD is a cyclic quadrilateral in which ∠BC

1.	In the adjoining figure, ABCD is a cyclic quadrilateral in which ∠BCD = 100° and ∠ABD = 50°. Find ∠ADB.
Answer» It is given that ABCD is a cyclic quadrilateral We know that the opposite angles of a cyclic quadrilateral are supplementary So we get ∠A + ∠C = 180^o By substituting the values ∠A + 100^o = 180^o On further calculation ∠A = 180^o – 100^o By subtraction ∠A = 80^o Consider △ ABD Using the angle sum property ∠A + ∠ABD + ∠ADB = 180^o By substituting the values 80^o + 50^o + ∠ADB = 180^o On further calculation ∠ADB = 180^o – 80^o – 50^o By subtraction ∠ADB = 180^o – 130^o So we get ∠ADB = 50^o Therefore, ∠ADB = 50^o.

In the adjoining figure, ABCD is a cyclic quadrilateral in which ∠BCD = 100° and ∠ABD = 50°. Find ∠ADB.

Answer»

It is given that ABCD is a cyclic quadrilateral

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

So we get

∠A + ∠C = 180^o

By substituting the values

∠A + 100^o = 180^o

On further calculation

∠A = 180^o – 100^o

By subtraction

∠A = 80^o

Consider △ ABD

Using the angle sum property

∠A + ∠ABD + ∠ADB = 180^o

By substituting the values

80^o + 50^o + ∠ADB = 180^o

On further calculation

∠ADB = 180^o – 80^o – 50^o

By subtraction

∠ADB = 180^o – 130^o

So we get

∠ADB = 50^o

Therefore, ∠ADB = 50^o.

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