Using the given information, find the value of x in the following figure :

Considering △ABC and △DBC,

∠BAC = ∠BDC = x° (∵ angles in same segment are equal.)

We know that sum of angles in a triangle is 180°.

Considering △ABC,

⇒ ∠BAC + ∠ABC + ∠BCA = 180°
⇒ x° + 69° + 31° = 180°
⇒ x° + 100° = 180°
⇒ x° = 180° - 100°
⇒ x° = 80°

Hence, the value of x = 80°.