Question

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

∠BCD= 100° and ∠ABD = 50°. Find ∠ADB.
​

Answer 1

Answer:

∠ADB=50°

Step-by-step explanation:

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°

By substituting the values

∠A+100°=180°

∠A=180°-100°

∠A=80°

Consider ΔABD

Using the angle sum property

∠A+∠ABD+∠ADB=180°

80°+50°+∠ADB=180°

∠ADB=180°-80°-50°

∠ADB=180°-130°

∠ADB=50°

Therefore,∠ADB=50°