In the given figure, if O is the centre of the circle, then the value of x is :

1. 40°

2. 50°

3. 70°

4. 30°

Join AC and BD.

∠BDC = 90° (Angle in semicircle is right angle)

OA = OB (Radii of same circle)

∠OBA = ∠OAB = 50° (Angles opposite to equal sides are equal in a triangle)

In triangle OAB,

∠AOB + ∠OAB + ∠OBA = 180°

∠AOB = 180° - (∠OAB + ∠OBA)

∠AOB = 180° - (50° + 50°)

∠AOB = 80°.

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

∠ACB = $\dfrac{1}{2}$ ∠AOB

∠ACB = $\dfrac{80°}{2}$

∠ACB = 40°

∠ADB = ∠ACB = 40° [Angle in same segment are equal]

From figure,

∠BDC = ∠ADB + x

90° = 40° + x

x = 50°.

Hence, option 2 is the correct option.