If ABCD is a cyclic quadrilateral with AB as the diameter of the circle and ∠ACD=50∘, then ∠BAD = ___.
40∘
Since an angle in a semicircle is a right angle, ∠ACB=90∘.
But, ∠BCD=∠ACD+∠ACB=50∘+90∘=140∘.
Consider the cyclic quadrilateral ABCD. Since opposite angles are supplementary,
∠BCD+∠DAB=180∘.
⟹∠BAD=180∘−140∘=40∘