If O is the center of the circle, find the value of x in the following figure (using the given information) :

AC subtends reflex angle ∠AOC at center and ∠ABC at point B. Since angle subtended at center is double the angle subtended at any other part of the circle.

⇒ Reflex ∠AOC = 2∠ABC …..(i)

From figure,

∠ABC + ∠CBD = 180° (As they are linear pair.)

∠ABC + 75° = 180°
∠ABC = 180° - 75°
∠ABC = 105°.

Putting value of ∠ABC = 105° in (i)

x° = 2(105°)
x° = 210°

Hence, the value of x = 210.