ABCD is a cyclic quadrilateral whose side AB is the diameter of the circle with centre O through A, B, C, D. If ∠ADC=130∘, Calculate ∠BAC.
40∘
∠ADC+∠ABC=180∘ (opposite angles are supplementary in a cyclic quadrilateral)
130∘+ ∠ABC=180∘
∠ABC=180∘−130∘
= 50∘
∠ACB=90∘ (Angle in a semi circle)
In ΔABC
∠ABC+∠BCA+∠BAC=180∘
50∘+90∘+∠BAC=180∘
∠ BAC = 180∘-140∘
= 40∘