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

From figure,

ABCD is a cyclic quadrilateral.

∠ACB = 90°. (∵ angle in semi circle is 90°)

Since sum of angles in triangle is 180°.

∴ In △ABC

⇒ ∠CAB + ∠ACB + ∠ABC = 180°
⇒ 25° + 90° + ∠ABC = 180°
⇒ 115° + ∠ABC = 180°
⇒ ∠ABC = 65°.

Since opposite angles sum is 180° in cyclic quadrilateral

⇒ ∠ABC + ∠ADC = 180°
⇒ 65° + x° = 180°
⇒ x° = 180° - 65°
⇒ x° = 115°.

Hence, the value of x = 115.