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Question
ABCD is a cyclic quadrilateral in a circle with centre O. If ∠ADC = 130°; find ∠BAC.
Solution
Here ∠ACB = 90°
(Angle in a semicircle is right angle)
Also, ∠ABC = 180° – ∠ADC = 180° – 130° = 50°
(Pair of opposite angles in a cyclic quadrilateral are supplementary)
By angle sum property of right triangle ACB,
∠BAC = 90° – ∠ABC = 90° – 50° = 40°
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