Given: AB is the diameter.
ABCD is the cyclic quadrilateral.
∠ADC = 130°
Since ABCD is the cyclic quadrilateral, therefore sum of opposite angles is 180°.
⇒ ∠ADC + ∠ABC = 180°
⇒ 130° + ∠ABC = 180°
⇒ ∠ABC = 180° - 130°
⇒ ∠ABC = 50°
Now, AB is the diameter and the angle subtended to the circle by the diameter is a right angle.
∴ ∠ACB = 90°
In triangle ACB, sum of all angles of triangle is 180°.
∴ ∠ACB + ∠ABC + ∠BAC = 180°
⇒ 90° + 50° + ∠BAC = 180°
⇒ ∠BAC = 180° - 90° - 50°
⇒ ∠BAC = 40°
