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

From figure,

⇒ ∠AOC + ∠COB = 180°
⇒ ∠COB = 180° - ∠AOC
⇒ ∠COB = 180° - 135°
⇒ ∠COB = 45°.

BC subtends ∠COB = 45° at center and ∠CDB = x° at point D. Since angle subtended at center is double the angle subtended at any other part of the circle.

⇒ ∠COB = 2∠CDB

⇒ 45° = 2x°

⇒ x° = $\dfrac{45\degree}{2} = 22\dfrac{1\degree}{2}.$

Hence, the value of x = $22\dfrac{1\degree}{2}$.