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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): In a ΔABC, ∠C = 3∠B = 2(∠A + ∠B), then ∠A = 20°.
Reason (R): The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°, then x = 85° and y = 55°.
- a)Both A and R are true and R is the correct explanation of A
- b)Both A and R are true but R is NOT the correct explanation of A
- c)A is true but R is false
- d)A is false and R is True
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Directions: In the following questions, A statement of Assertion (A) ...
Assertion (A): In a ΔABC, ∠C = 3∠B = 2(∠A + ∠B), then ∠A = 20°.
Reason (R): The angles of a triangle are x, y, and 40°. The difference between the two angles x and y is 30°, then x = 85° and y = 55°.
Explanation:
To find the value of ∠A, we need to solve the equation given in the assertion part.
Assertion: ∠C = 3∠B = 2(∠A + ∠B)
Let's assume ∠A = x, ∠B = y, and ∠C = z.
So, from the given equation:
z = 3y (1)
z = 2(x + y) (2)
From equation (1), we can substitute the value of z in equation (2):
3y = 2(x + y)
Simplifying the equation:
3y - 2y = 2x
y = 2x (3)
Now, let's move to the reason part of the question.
Reason: The angles of a triangle are x, y, and 40°. The difference between the two angles x and y is 30°, then x = 85° and y = 55°.
Let's assume x = 85° and y = 55°.
If the difference between x and y is 30°:
x - y = 30°
85° - 55° = 30°
Therefore, the reason given in the question is correct.
Now, let's compare the values of x and y obtained from the reason part with the values obtained from the assertion part.
From the assertion part:
y = 2x
From the reason part:
x = 85° and y = 55°
Substituting the values in the equation:
55° = 2(85°)
Simplifying the equation:
55° = 170°
The equation is not true as 55° is not equal to 170°.
Hence, the reason given in the question is not the correct explanation of the assertion.
Therefore, the correct answer is option 'B' - Both A and R are true but R is NOT the correct explanation of A.
Reason (R): The angles of a triangle are x, y, and 40°. The difference between the two angles x and y is 30°, then x = 85° and y = 55°.
Explanation:
To find the value of ∠A, we need to solve the equation given in the assertion part.
Assertion: ∠C = 3∠B = 2(∠A + ∠B)
Let's assume ∠A = x, ∠B = y, and ∠C = z.
So, from the given equation:
z = 3y (1)
z = 2(x + y) (2)
From equation (1), we can substitute the value of z in equation (2):
3y = 2(x + y)
Simplifying the equation:
3y - 2y = 2x
y = 2x (3)
Now, let's move to the reason part of the question.
Reason: The angles of a triangle are x, y, and 40°. The difference between the two angles x and y is 30°, then x = 85° and y = 55°.
Let's assume x = 85° and y = 55°.
If the difference between x and y is 30°:
x - y = 30°
85° - 55° = 30°
Therefore, the reason given in the question is correct.
Now, let's compare the values of x and y obtained from the reason part with the values obtained from the assertion part.
From the assertion part:
y = 2x
From the reason part:
x = 85° and y = 55°
Substituting the values in the equation:
55° = 2(85°)
Simplifying the equation:
55° = 170°
The equation is not true as 55° is not equal to 170°.
Hence, the reason given in the question is not the correct explanation of the assertion.
Therefore, the correct answer is option 'B' - Both A and R are true but R is NOT the correct explanation of A.
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Community Answer
Directions: In the following questions, A statement of Assertion (A) ...
In case of assertion
Given that, ∠C = 3∠B = 2(∠A + ∠B)
3∠B = 2(∠A + ∠B)
3∠B = 2∠A + 2∠B
∠B = 2∠A
2 ∠A − ∠B = 0 ...(i)
We know that the sum of the measures of all angles of a triangle is 180°.
Therefore, ∠A + ∠B + ∠C = 180°
∠A + ∠B + 3∠B = 180°
∠A + 4∠B = 180° ...(ii)
Multiplying equation (i) by 4, we obtain
8∠A − 4∠B = 0 ...(iii)
Adding equations (ii) and (iii), we obtain
9∠A = 180°
∠A = 20°
∴ Assertion is correct.
In case of reason: Given that, x, y and 40° are the angels of a triangle.
x + y + 40° = 180°
[Since the sum of all the angels of a triangle is 180°.]
⇒ x + y = 140° ...(i)
Also, x – y = 30° ...(ii)
On adding Eqs. (i) and (ii), we get
2x = 170°
⇒ x = 170/2
∴ x = 85°
On putting x = 85° in Eq. (i), we get
85° + y = 140°
y = 140° – 85° = 55°
∴ y = 55°
Hence, the required values of x and y are 85° and 55°, respectively.
∴ Reason is correct.
Hence, both assertion and reason are correct but reason is not the correct explanation for assertion.
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): In a ΔABC, ∠C = 3∠B = 2(∠A + ∠B), then ∠A = 20°.Reason (R): The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°, then x = 85° and y = 55°.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'B'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): In a ΔABC, ∠C = 3∠B = 2(∠A + ∠B), then ∠A = 20°.Reason (R): The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°, then x = 85° and y = 55°.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): In a ΔABC, ∠C = 3∠B = 2(∠A + ∠B), then ∠A = 20°.Reason (R): The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°, then x = 85° and y = 55°.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'B'. Can you explain this answer?.
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): In a ΔABC, ∠C = 3∠B = 2(∠A + ∠B), then ∠A = 20°.Reason (R): The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°, then x = 85° and y = 55°.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'B'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): In a ΔABC, ∠C = 3∠B = 2(∠A + ∠B), then ∠A = 20°.Reason (R): The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°, then x = 85° and y = 55°.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): In a ΔABC, ∠C = 3∠B = 2(∠A + ∠B), then ∠A = 20°.Reason (R): The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°, then x = 85° and y = 55°.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): In a ΔABC, ∠C = 3∠B = 2(∠A + ∠B), then ∠A = 20°.Reason (R): The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°, then x = 85° and y = 55°.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): In a ΔABC, ∠C = 3∠B = 2(∠A + ∠B), then ∠A = 20°.Reason (R): The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°, then x = 85° and y = 55°.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): In a ΔABC, ∠C = 3∠B = 2(∠A + ∠B), then ∠A = 20°.Reason (R): The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°, then x = 85° and y = 55°.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): In a ΔABC, ∠C = 3∠B = 2(∠A + ∠B), then ∠A = 20°.Reason (R): The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°, then x = 85° and y = 55°.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): In a ΔABC, ∠C = 3∠B = 2(∠A + ∠B), then ∠A = 20°.Reason (R): The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°, then x = 85° and y = 55°.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Class 10 tests.
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