In the given figure, O is centre of the circle.
If ∠AOC = 130°, then the value of x is :

1. 25°

2. 50°

3. 65°

4. 40°

Join AD.

∠AOC = 130°

∠ADB = 90°

We know that,

The angle which an arc subtends at the center is double that which it subtends at any point on the remaining part of the circumference.

∴ ∠ADC = $\dfrac{1}{2}$ ∠AOC

∠ADC = $\dfrac{130^{\circ}}{2}$ = 65°

At point D,

∠ADB = ∠ADC + ∠CDB

90° = 65° + x

x = 25°

Hence, option 1 is the correct option.