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Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer as
Assertion : In a cyclic quadrilateral ABCD, ∠A - ∠C = 60º, then the smaller of two is 60º.
Reason : Opposite angles of cyclic quadrilateral are supplementary.
- a)Both assertion and reason are true and reason is the correct explanation of assertion.
- b)Both assertion and reason are true but reason is not the correct explanation of assertion.
- c)Assertion is true but reason is false.
- d)Assertion is false but reason is true
Correct answer is option 'A'. Can you explain this answer?
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Direction: In the following questions, a statement of Assertion is gi...
Since ABCD is a cyclic quadrilateral, so, its opposite angles are supplementary
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∠A + ∠C = 180º ...(1)
Also, ∠A - ∠C = 60º ...(2)
On solving (i) and (ii), we get
∠A = 120º, ∠C = 60º
Most Upvoted Answer
Direction: In the following questions, a statement of Assertion is gi...
Assertion : In a cyclic quadrilateral ABCD, ∠A - ∠C = 60º, then the smaller of the two is 60º.
Reason : Opposite angles of a cyclic quadrilateral are supplementary.
To understand this question, let's first define a cyclic quadrilateral and understand its properties.
A cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. In other words, the four corners of the quadrilateral touch the circumference of a circle.
Properties of a Cyclic Quadrilateral:
1. The opposite angles of a cyclic quadrilateral are supplementary, which means they add up to 180 degrees.
2. The sum of the measures of the opposite angles in a cyclic quadrilateral is always 180 degrees.
In this question, it is given that ∠A - ∠C = 60º. We need to determine if the smaller angle between the two is 60º or not.
Explanation:
Let's assume that ∠A is the larger angle between the two, and ∠C is the smaller angle.
According to the given information, ∠A - ∠C = 60º.
Since the opposite angles of a cyclic quadrilateral are supplementary, we can write the equation as ∠A + ∠D = 180º, where ∠D is the opposite angle of ∠A.
Now, let's substitute the value of ∠D in terms of ∠C using the equation ∠A - ∠C = 60º.
∠D = 180º - ∠A (opposite angles are supplementary)
∠D = 180º - (∠C + 60º) (substituting the value of ∠A from the given equation)
Simplifying, we get:
∠D = 120º - ∠C
Now, we have ∠C and ∠D in terms of each other.
Since ABCD is a cyclic quadrilateral, the sum of the measures of the opposite angles (∠C and ∠D) is 180 degrees.
Therefore, we can write the equation as:
∠C + ∠D = 180º
Substituting the values of ∠C and ∠D, we get:
∠C + (120º - ∠C) = 180º
Simplifying, we get:
120º = 180º
This is not possible, as the sum of two angles cannot be greater than 180 degrees.
Hence, the assumption that ∠A is the larger angle is incorrect.
Therefore, the smaller of the two angles is indeed 60º, as stated in the assertion.
Hence, option A is the correct answer.
Reason : Opposite angles of a cyclic quadrilateral are supplementary.
To understand this question, let's first define a cyclic quadrilateral and understand its properties.
A cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. In other words, the four corners of the quadrilateral touch the circumference of a circle.
Properties of a Cyclic Quadrilateral:
1. The opposite angles of a cyclic quadrilateral are supplementary, which means they add up to 180 degrees.
2. The sum of the measures of the opposite angles in a cyclic quadrilateral is always 180 degrees.
In this question, it is given that ∠A - ∠C = 60º. We need to determine if the smaller angle between the two is 60º or not.
Explanation:
Let's assume that ∠A is the larger angle between the two, and ∠C is the smaller angle.
According to the given information, ∠A - ∠C = 60º.
Since the opposite angles of a cyclic quadrilateral are supplementary, we can write the equation as ∠A + ∠D = 180º, where ∠D is the opposite angle of ∠A.
Now, let's substitute the value of ∠D in terms of ∠C using the equation ∠A - ∠C = 60º.
∠D = 180º - ∠A (opposite angles are supplementary)
∠D = 180º - (∠C + 60º) (substituting the value of ∠A from the given equation)
Simplifying, we get:
∠D = 120º - ∠C
Now, we have ∠C and ∠D in terms of each other.
Since ABCD is a cyclic quadrilateral, the sum of the measures of the opposite angles (∠C and ∠D) is 180 degrees.
Therefore, we can write the equation as:
∠C + ∠D = 180º
Substituting the values of ∠C and ∠D, we get:
∠C + (120º - ∠C) = 180º
Simplifying, we get:
120º = 180º
This is not possible, as the sum of two angles cannot be greater than 180 degrees.
Hence, the assumption that ∠A is the larger angle is incorrect.
Therefore, the smaller of the two angles is indeed 60º, as stated in the assertion.
Hence, option A is the correct answer.
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Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : In a cyclic quadrilateral ABCD, ∠A - ∠C = 60º, then the smaller of two is 60º.Reason : Opposite angles of cyclic quadrilateral are supplementary.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is trueCorrect answer is option 'A'. Can you explain this answer?
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Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : In a cyclic quadrilateral ABCD, ∠A - ∠C = 60º, then the smaller of two is 60º.Reason : Opposite angles of cyclic quadrilateral are supplementary.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is trueCorrect answer is option 'A'. Can you explain this answer? 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 Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : In a cyclic quadrilateral ABCD, ∠A - ∠C = 60º, then the smaller of two is 60º.Reason : Opposite angles of cyclic quadrilateral are supplementary.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is trueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : In a cyclic quadrilateral ABCD, ∠A - ∠C = 60º, then the smaller of two is 60º.Reason : Opposite angles of cyclic quadrilateral are supplementary.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is trueCorrect answer is option 'A'. Can you explain this answer?.
Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : In a cyclic quadrilateral ABCD, ∠A - ∠C = 60º, then the smaller of two is 60º.Reason : Opposite angles of cyclic quadrilateral are supplementary.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is trueCorrect answer is option 'A'. Can you explain this answer? 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 Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : In a cyclic quadrilateral ABCD, ∠A - ∠C = 60º, then the smaller of two is 60º.Reason : Opposite angles of cyclic quadrilateral are supplementary.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is trueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : In a cyclic quadrilateral ABCD, ∠A - ∠C = 60º, then the smaller of two is 60º.Reason : Opposite angles of cyclic quadrilateral are supplementary.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is trueCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : In a cyclic quadrilateral ABCD, ∠A - ∠C = 60º, then the smaller of two is 60º.Reason : Opposite angles of cyclic quadrilateral are supplementary.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is trueCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
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