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Abcd is a Cyclic Quadrilateral in a Circle with Centre O. If ∠Adc = 130°; Find ∠ Bac. - Mathematics

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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 cy clic quadrilateral are supplementary)
By angle sum property of right triangle ACB,
∠BAC = 90° - ∠ABC = 90° - 50° = 40°

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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 17: Circles
Exercise 17(A) | Q: 13 | Page no. 258
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Abcd is a Cyclic Quadrilateral in a Circle with Centre O. If ∠Adc = 130°; Find ∠ Bac. Concept: Cyclic Properties.
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