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ABCD is a cyclic quadrilateral such that side AB is the diameter of the circle and angle ADC=140 degree.The value of angle BAC is?
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Problem:
ABCD is a cyclic quadrilateral such that side AB is the diameter of the circle and angle ADC=140 degree. The value of angle BAC is?
Solution:
Properties of a Cyclic Quadrilateral
A cyclic quadrilateral is a quadrilateral that can be inscribed in a circle. The following properties apply to cyclic quadrilaterals:
- Opposite angles of a cyclic quadrilateral are supplementary (add up to 180 degrees).
- The angles in the same segment of a circle are equal.
Angle ADC and Angle ABC
Since AB is the diameter of the circle, angle ABC is a right angle (90 degrees).
From the properties of a cyclic quadrilateral, we know that angle ADC + angle ABC = 180 degrees.
Therefore, angle ADC = 140 degrees, and angle ABC = 40 degrees.
Angle BAC
Angle BAC is an angle in the same segment as angle ABC.
From the properties of a cyclic quadrilateral, we know that the angles in the same segment of a circle are equal.
Therefore, angle BAC = angle ABC = 40 degrees.
Final Answer:
The value of angle BAC is 40 degrees.
ABCD is a cyclic quadrilateral such that side AB is the diameter of the circle and angle ADC=140 degree. The value of angle BAC is?
Solution:
Properties of a Cyclic Quadrilateral
A cyclic quadrilateral is a quadrilateral that can be inscribed in a circle. The following properties apply to cyclic quadrilaterals:
- Opposite angles of a cyclic quadrilateral are supplementary (add up to 180 degrees).
- The angles in the same segment of a circle are equal.
Angle ADC and Angle ABC
Since AB is the diameter of the circle, angle ABC is a right angle (90 degrees).
From the properties of a cyclic quadrilateral, we know that angle ADC + angle ABC = 180 degrees.
Therefore, angle ADC = 140 degrees, and angle ABC = 40 degrees.
Angle BAC
Angle BAC is an angle in the same segment as angle ABC.
From the properties of a cyclic quadrilateral, we know that the angles in the same segment of a circle are equal.
Therefore, angle BAC = angle ABC = 40 degrees.
Final Answer:
The value of angle BAC is 40 degrees.
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ABCD is a cyclic quadrilateral such that side AB is the diameter of the circle and angle ADC=140 degree.The value of angle BAC is?
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ABCD is a cyclic quadrilateral such that side AB is the diameter of the circle and angle ADC=140 degree.The value of angle BAC is? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about ABCD is a cyclic quadrilateral such that side AB is the diameter of the circle and angle ADC=140 degree.The value of angle BAC is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a cyclic quadrilateral such that side AB is the diameter of the circle and angle ADC=140 degree.The value of angle BAC is?.
ABCD is a cyclic quadrilateral such that side AB is the diameter of the circle and angle ADC=140 degree.The value of angle BAC is? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about ABCD is a cyclic quadrilateral such that side AB is the diameter of the circle and angle ADC=140 degree.The value of angle BAC is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a cyclic quadrilateral such that side AB is the diameter of the circle and angle ADC=140 degree.The value of angle BAC is?.
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