Question

Find the ∠ADE, if ∠BDF = 60° and ADB is the tangent to the circle with centre C.

Options

• 30°

• 60°

• 45°

• 90°

Answer 1

30°

Explanation:

Given: ∠BDF = 60°.

Now, EF is the circle's diameter and the angle in a semi-circle is a right angle.

So, ∠EDF = 90°

Now, ∠ADE + ∠EDF + ∠BDF =  180°  ......[Linear pair]

⇒ ∠ADE + 90° + 60° = 180°

⇒ ∠ADE = 180° – 90° – 60° = 30°

Thus, the value of ∠ADE is 30°.