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ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and angle ADC = 140. Then angle BAC is equal to. Figure given below.?
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ABCD is a cyclic quadrilateral such that AB is a diameter of the circl...
Explanation:
Given, ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and angle ADC = 140.
Properties of a Cyclic Quadrilateral:
- A quadrilateral is cyclic if and only if the opposite angles are supplementary.
- In a cyclic quadrilateral, the exterior angle is equal to the interior opposite angle.
Using the Properties:
- As AB is the diameter of the circle, angle ABD is 90 degrees.
- Therefore, angle ABC is also 90 degrees as opposite angles in a cyclic quadrilateral are supplementary.
- Also, angle ADC is given as 140 degrees.
- Therefore, angle BDC is 180 - 140 = 40 degrees as opposite angles in a cyclic quadrilateral are supplementary.
- Now, in triangle ABD, angle ABD is 90 degrees and angle BDC is 40 degrees.
- Therefore, angle BAD is 180 - 90 - 40 = 50 degrees using the angle sum property of a triangle.
- Finally, in triangle BAC, angle BAC is equal to angle BAD as they are opposite angles in a cyclic quadrilateral.
- Therefore, angle BAC is also 50 degrees.
Hence, angle BAC is 50 degrees.
Given, ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and angle ADC = 140.
Properties of a Cyclic Quadrilateral:
- A quadrilateral is cyclic if and only if the opposite angles are supplementary.
- In a cyclic quadrilateral, the exterior angle is equal to the interior opposite angle.
Using the Properties:
- As AB is the diameter of the circle, angle ABD is 90 degrees.
- Therefore, angle ABC is also 90 degrees as opposite angles in a cyclic quadrilateral are supplementary.
- Also, angle ADC is given as 140 degrees.
- Therefore, angle BDC is 180 - 140 = 40 degrees as opposite angles in a cyclic quadrilateral are supplementary.
- Now, in triangle ABD, angle ABD is 90 degrees and angle BDC is 40 degrees.
- Therefore, angle BAD is 180 - 90 - 40 = 50 degrees using the angle sum property of a triangle.
- Finally, in triangle BAC, angle BAC is equal to angle BAD as they are opposite angles in a cyclic quadrilateral.
- Therefore, angle BAC is also 50 degrees.
Hence, angle BAC is 50 degrees.
Community Answer
ABCD is a cyclic quadrilateral such that AB is a diameter of the circl...
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ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and angle ADC = 140. Then angle BAC is equal to. Figure given below.?
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ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and angle ADC = 140. Then angle BAC is equal to. Figure given below.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and angle ADC = 140. Then angle BAC is equal to. Figure given below.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and angle ADC = 140. Then angle BAC is equal to. Figure given below.?.
ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and angle ADC = 140. Then angle BAC is equal to. Figure given below.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and angle ADC = 140. Then angle BAC is equal to. Figure given below.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and angle ADC = 140. Then angle BAC is equal to. Figure given below.?.
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