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

Considering △ACB and △ADB,

∠ACB = ∠ADB = x° (∵ angles in same segment are equal.)

Considering △ACB,

∠ABC = 90° (∵ angle in semicircle is 90°.)

Since sum of angles in a triangle is equal to 180°.

⇒ ∠BAC + ∠ACB + ∠ABC = 180°.
⇒ 40° + x° + 90° = 180°
⇒ x° + 130° = 180°
⇒ x° = 50°.

Hence, the value of x = 50°.