ABCD is a cyclic quadrilateral whose side AB is a diameter of the circle through A,B,C,D.
The given information can be represented using a figure as:
Here, O is the centre of the circle.
ADCBOA is a semicircle
∴ ∠ADB = 90°
Given that ∠ADC = 130°
⇒ ∠ADB + ∠BDC = 130°
⇒ ∠BDC = 130° – 90° = 40°
∠BAC and ∠BDC are the angles in the same segment
∴ ∠BAC = ∠BDC
⇒ ∠BAC = 40°
Thus, the measure of ∠BAC is 40°