CAT Exam > CAT Questions > DIRECTIONSfor the question:Solve the followin...
Start Learning for Free
DIRECTIONS for the question: Solve the following question and mark the best possible option.
The measure of the largest angle in a triangle is twice the sum of the measures of the other two angles. What is the largest value of the smallest angle of the triangle?
- a)π/3°
- b)π/2°
- c)π/6°
- d)π/4°
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
DIRECTIONSfor the question:Solve the following question and mark the b...
►If the sum of the two smaller angles is x, then the largest angle will be 2x.
►Since the sum of all angles is 180°, we get x = 60°.
►The largest value of the smallest angle will make it equal to the other angle.
Thus the largest value of the smallest angle in the triangle will be 30° = π/6°.
Thus the largest value of the smallest angle in the triangle will be 30° = π/6°.
Most Upvoted Answer
DIRECTIONSfor the question:Solve the following question and mark the b...
Explanation:
Given:
- Let the measures of the angles be A, B, and C in the triangle.
- The largest angle, let's say A, is twice the sum of the other two angles, i.e., A = 2(B + C).
Sum of angles in a triangle:
- The sum of all angles in a triangle is always equal to 180 degrees. Therefore, A + B + C = 180.
Substitution:
- Substituting the value of A from the given information into the sum of angles equation, we get 2(B + C) + B + C = 180.
- Simplifying the equation, we get 3B + 3C = 180, which can be further simplified to B + C = 60.
Maximum value of the smallest angle:
- To find the largest value of the smallest angle, we need to minimize the sum of the other two angles (B + C).
- The minimum value of B + C occurs when B = C (to minimize the sum while keeping A = 2(B + C)).
- Therefore, B = C = 30 degrees.
Final answer:
- The largest value of the smallest angle of the triangle is 30 degrees, which is equivalent to π/6 radians.
- Hence, the correct answer is option 'c) π/6°'.
Given:
- Let the measures of the angles be A, B, and C in the triangle.
- The largest angle, let's say A, is twice the sum of the other two angles, i.e., A = 2(B + C).
Sum of angles in a triangle:
- The sum of all angles in a triangle is always equal to 180 degrees. Therefore, A + B + C = 180.
Substitution:
- Substituting the value of A from the given information into the sum of angles equation, we get 2(B + C) + B + C = 180.
- Simplifying the equation, we get 3B + 3C = 180, which can be further simplified to B + C = 60.
Maximum value of the smallest angle:
- To find the largest value of the smallest angle, we need to minimize the sum of the other two angles (B + C).
- The minimum value of B + C occurs when B = C (to minimize the sum while keeping A = 2(B + C)).
- Therefore, B = C = 30 degrees.
Final answer:
- The largest value of the smallest angle of the triangle is 30 degrees, which is equivalent to π/6 radians.
- Hence, the correct answer is option 'c) π/6°'.
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
DIRECTIONSfor the question:Solve the following question and mark the best possible option.The measure of the largest angle in a triangle is twice the sum of the measures of the other two angles. What is the largest value of the smallest angle of the triangle?a)π/3°b)π/2°c)π/6°d)π/4°Correct answer is option 'C'. Can you explain this answer?
Question Description
DIRECTIONSfor the question:Solve the following question and mark the best possible option.The measure of the largest angle in a triangle is twice the sum of the measures of the other two angles. What is the largest value of the smallest angle of the triangle?a)π/3°b)π/2°c)π/6°d)π/4°Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about DIRECTIONSfor the question:Solve the following question and mark the best possible option.The measure of the largest angle in a triangle is twice the sum of the measures of the other two angles. What is the largest value of the smallest angle of the triangle?a)π/3°b)π/2°c)π/6°d)π/4°Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONSfor the question:Solve the following question and mark the best possible option.The measure of the largest angle in a triangle is twice the sum of the measures of the other two angles. What is the largest value of the smallest angle of the triangle?a)π/3°b)π/2°c)π/6°d)π/4°Correct answer is option 'C'. Can you explain this answer?.
DIRECTIONSfor the question:Solve the following question and mark the best possible option.The measure of the largest angle in a triangle is twice the sum of the measures of the other two angles. What is the largest value of the smallest angle of the triangle?a)π/3°b)π/2°c)π/6°d)π/4°Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about DIRECTIONSfor the question:Solve the following question and mark the best possible option.The measure of the largest angle in a triangle is twice the sum of the measures of the other two angles. What is the largest value of the smallest angle of the triangle?a)π/3°b)π/2°c)π/6°d)π/4°Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONSfor the question:Solve the following question and mark the best possible option.The measure of the largest angle in a triangle is twice the sum of the measures of the other two angles. What is the largest value of the smallest angle of the triangle?a)π/3°b)π/2°c)π/6°d)π/4°Correct answer is option 'C'. Can you explain this answer?.
Solutions for DIRECTIONSfor the question:Solve the following question and mark the best possible option.The measure of the largest angle in a triangle is twice the sum of the measures of the other two angles. What is the largest value of the smallest angle of the triangle?a)π/3°b)π/2°c)π/6°d)π/4°Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of DIRECTIONSfor the question:Solve the following question and mark the best possible option.The measure of the largest angle in a triangle is twice the sum of the measures of the other two angles. What is the largest value of the smallest angle of the triangle?a)π/3°b)π/2°c)π/6°d)π/4°Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
DIRECTIONSfor the question:Solve the following question and mark the best possible option.The measure of the largest angle in a triangle is twice the sum of the measures of the other two angles. What is the largest value of the smallest angle of the triangle?a)π/3°b)π/2°c)π/6°d)π/4°Correct answer is option 'C'. Can you explain this answer?, a detailed solution for DIRECTIONSfor the question:Solve the following question and mark the best possible option.The measure of the largest angle in a triangle is twice the sum of the measures of the other two angles. What is the largest value of the smallest angle of the triangle?a)π/3°b)π/2°c)π/6°d)π/4°Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of DIRECTIONSfor the question:Solve the following question and mark the best possible option.The measure of the largest angle in a triangle is twice the sum of the measures of the other two angles. What is the largest value of the smallest angle of the triangle?a)π/3°b)π/2°c)π/6°d)π/4°Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice DIRECTIONSfor the question:Solve the following question and mark the best possible option.The measure of the largest angle in a triangle is twice the sum of the measures of the other two angles. What is the largest value of the smallest angle of the triangle?a)π/3°b)π/2°c)π/6°d)π/4°Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup