ABCD is a cyclic quadrilateral whose side AB is a diameter of the circle through A, B, C and D. If ∠ADC=130∘, find ∠BAC.
(1203)∘
40∘
Given: ABCD is a cyclic quadrilateral whose side AB is the diameter of the circle and ∠ADC=130∘.
To find ∠BAC,
∠D+∠B=180∘(Opposite angles of a cyclic quadilateral )
130∘+∠B=180∘
∠B=180∘−130∘=50∘
∠ACB=90∘(Angle in a semicircle)
In ΔABC,
∠BAC+50∘+90∘=180∘(Since sum of angles of a triangle is 180∘)
∠BAC=180∘−90∘−50∘=40∘