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Question
ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 140º, then ∠BAC is equal to ______.
Options
80º
50º
40º
30º
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Solution
ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 140º, then ∠BAC is equal to 50º.
Explanation:
Given, ABCD is a cyclic quadrilateral and ∠ADC = 140°.
We know that, sum of the opposite angles in a cyclic quadrilateral is 180°.
∠ADC + ∠ABC = 180°
⇒ 140° + ∠ABC = 180°
⇒ ∠ABC = 180° – 140°
∴ ∠ABC = 40°
Since, ∠ACB is an angle in a semi-circle.
∴ ∠ACB = 90°
In ΔABC, ∠BAC + ∠ACB + ∠ABC = 180° ...[By angle sum property of a triangle]
⇒ ∠BAC + 90° + 40° = 180°
⇒ ∠BAC = 180° – 130° = 50°
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