ABCD is a cycle quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 158°. Then ∠BAC is equal to:
Show answer & explanation
Correct answer: D
Explanation
Correct Answer is option 4 i.e. 68°
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Understanding |
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Given: ∠ADC = 158° |
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Application |
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We know that in cyclic quadrilateral the sum of opposite angle = 180° ⇒ ∠ABC + ∠ADC = 180° ⇒ ∠ABC + 158° = 180° ⇒ ∠ABC = 180° − 158° = 22° In ΔABC We know that angle made by diameter on the circumference is 90° ∴ ∠ACB = 90° Now, ∠BAC + ∠ABC + ∠ACB = 180° ⇒ ∠BAC + 22° + 90° = 180° ⇒ ∠BAC = 180 – 112 = 68° |