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In a ΔABC, if 2∠A = 3∠B = 6∠C, Then ∠A is equal to:
- a)60°
- b)30°
- c)90°
- d)120°
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
In a ΔABC, if 2∠A = 3∠B = 6∠C, Then ∠A is equal ...
Let us assume 2∠A = 3∠B = 6∠C = K
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In a ΔABC, if 2∠A = 3∠B = 6∠C, Then ∠A is equal ...
Given Information:
In triangle ΔABC, 2∠A = 3∠B = 6∠C
Solution:
Step 1: Finding the sum of angles in a triangle
In a triangle, the sum of all interior angles is always 180°.
Step 2: Expressing angles in terms of ∠A
Given, 2∠A = 3∠B = 6∠C
Let's express angles B and C in terms of angle A:
2∠A = 3∠B
∠B = 2/3∠A
Also,
2∠A = 6∠C
∠C = 1/3∠A
Step 3: Substituting angle values in the sum of angles formula
Now, substitute the expressions for ∠B and ∠C in terms of ∠A into the formula for the sum of angles in a triangle:
∠A + ∠B + ∠C = 180°
∠A + 2/3∠A + 1/3∠A = 180°
(6/3)∠A = 180°
2∠A = 180°
∠A = 90°
Therefore, ∠A is equal to 90° (option c).
In triangle ΔABC, 2∠A = 3∠B = 6∠C
Solution:
Step 1: Finding the sum of angles in a triangle
In a triangle, the sum of all interior angles is always 180°.
Step 2: Expressing angles in terms of ∠A
Given, 2∠A = 3∠B = 6∠C
Let's express angles B and C in terms of angle A:
2∠A = 3∠B
∠B = 2/3∠A
Also,
2∠A = 6∠C
∠C = 1/3∠A
Step 3: Substituting angle values in the sum of angles formula
Now, substitute the expressions for ∠B and ∠C in terms of ∠A into the formula for the sum of angles in a triangle:
∠A + ∠B + ∠C = 180°
∠A + 2/3∠A + 1/3∠A = 180°
(6/3)∠A = 180°
2∠A = 180°
∠A = 90°
Therefore, ∠A is equal to 90° (option c).
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In a ΔABC, if 2∠A = 3∠B = 6∠C, Then ∠A is equal to:a)60°b)30°c)90°d)120°Correct answer is option 'C'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about In a ΔABC, if 2∠A = 3∠B = 6∠C, Then ∠A is equal to:a)60°b)30°c)90°d)120°Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a ΔABC, if 2∠A = 3∠B = 6∠C, Then ∠A is equal to:a)60°b)30°c)90°d)120°Correct answer is option 'C'. Can you explain this answer?.
In a ΔABC, if 2∠A = 3∠B = 6∠C, Then ∠A is equal to:a)60°b)30°c)90°d)120°Correct answer is option 'C'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about In a ΔABC, if 2∠A = 3∠B = 6∠C, Then ∠A is equal to:a)60°b)30°c)90°d)120°Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a ΔABC, if 2∠A = 3∠B = 6∠C, Then ∠A is equal to:a)60°b)30°c)90°d)120°Correct answer is option 'C'. Can you explain this answer?.
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