Theorem of Equal Chords Subtending Equal Angles at the Center
If ABCD is a ...
Question
If ABCD is a cyclic quadrilateral with AB as the diameter of the circle and ∠ACD=50∘, then ∠BAD = ___ degrees.
40
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Solution
The correct option is A 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∘