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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

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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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