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

Angle of a circle is 360°.

⇒ ∠AOB + ∠AOC + ∠BOC = 360°
⇒ ∠AOB + 80° + 130° = 360°
⇒ ∠AOB + 210° = 360°
⇒ ∠AOB = 360° - 210°
⇒ ∠AOB = 150°.

From figure,

⇒ ∠AOB = 2∠ACB (∵ angle subtended by an arc at the center = double the angle subtended by it any point on the remaining part of the circle.)

⇒ 150° = 2∠ACB
⇒ ∠ACB = $\dfrac{150°}{2}$
⇒ ∠ACB = 75°
⇒ x° = 75°.

Hence, the value of x = 75°.