2. ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 150∘ . Then ∠BAC is equal to
Question
2. AB is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 150°. Then ∠BAC is equal to
Solution
In a cyclic quadrilateral, the sum of opposite angles is 180 degrees.
Given that ∠ADC = 150 degrees, and since AB is the diameter of the circle, ∠BAC is the angle subtended by the diameter at the circumference, which is always 90 degrees (a property of a circle).
However, since ∠ADC and ∠BAC are opposite angles in cyclic quadrilateral ABCD, their sum should be 180 degrees.
So, if ∠ADC = 150 degrees, then ∠BAC = 180 - 150 = 30 degrees.
Therefore, ∠BAC = 30 degrees.
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