Question

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

Answer 1

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.