Mathematics
ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 125°, then ∠BAC is equal to :
35°
40°
45°
55°
Answer
Opposite angles of a cyclic quadrilateral are supplementary.
So,
∠ABC + ∠ADC = 180°
∠ABC = 180° − 125° = 55°.
∠ACB = 90° [Angle in semicircle is a right angle]
In △ABC,
By angle sum property of triangle,
∠BAC + ∠ABC + ∠ACB = 180°
∠BAC + 55° + 90° = 180°
∠BAC = 180° − 145° = 35°.
Hence, option 1 is the correct option.
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