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.

By property of cyclic quadrilateral — An exterior angle of cyclic quadrilateral is equal to opposite interior angle.

We get,

∠BAD = ∠DCE = x°

Arc BD subtends ∠BOD on center and ∠BAD at point A of the circle.

∴ ∠BOD = 2∠BAD (∵ as angle subtended on center of circle is double the angle subtended on any other part.)

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

Hence, the value of x = 75.