ABCD is a cyclic quadrilateral whose side AB is a diameter of the circle through A, B, C and D. If ∠ADC=130∘, then find ∠BAC.
Given: ABCD is a cyclic quadrilateral whose side AB is the diameter of the circle and ∠ADC=130∘.
To find ∠BAC:
Since opposite angles of a cyclic quadilateral are supplementary, we have
∠D+∠B=180∘.
i.e., 130∘+∠B=180∘
⟹∠B=180∘−130∘=50∘
Since an angle in a semicircle is a right angle, we have
∠ACB=90∘.
In ΔABC,
∠BAC+50∘+90∘=180∘. (Angle sum property)
⟹∠BAC=180∘−90∘−50∘=40∘