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The angles of a triangle in A.P. the smallest being half of the greatest. So what are the angles ?
- a)45°, 55°, 90°
- b)50°, 25°, 75°
- c)60°, 40°, 80°
- d)40°, 60°, 30°
Correct answer is 'C'. Can you explain this answer?
Most Upvoted Answer
The angles of a triangle in A.P. the smallest being half of the greate...
Let a-d, a, a+d be the three angles of the triangle that form AP.Now, 2(a-d)=a+d2a-2d=a+da=3d (eq. 1)Now by angle sum property,(a-d)+a+(a+d)=1803a=180a=60 (eq.2)from (1) and (2),3d=60d=20Now, the angles are,a-d=60-20=40a=60a+d=60+20=80
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The angles of a triangle in A.P. the smallest being half of the greate...
Let the angles of the triangle be A, B, and C, with A being the smallest angle and C being the greatest angle.
Given that the angles are in an arithmetic progression (A.P.), we have the following relationship:
B = (A+C)/2
Since the smallest angle is half of the greatest angle, we have:
A = (1/2)C
Substituting this value of A in the first equation, we get:
B = [(1/2)C + C]/2
B = (3/2)C/2
B = (3/4)C
Now, we know that the sum of the angles in a triangle is 180 degrees. So, we can write the equation:
A + B + C = 180
Substituting the values of A and B, we get:
(1/2)C + (3/4)C + C = 180
(4/8)C + (6/8)C + (8/8)C = 180
(18/8)C = 180
C = (8/18) * 180
C = 80 degrees
Using this value of C, we can find the other angles:
A = (1/2)C = (1/2) * 80 = 40 degrees
B = (3/4)C = (3/4) * 80 = 60 degrees
Therefore, the angles of the triangle are 40 degrees, 60 degrees, and 80 degrees.
Given that the angles are in an arithmetic progression (A.P.), we have the following relationship:
B = (A+C)/2
Since the smallest angle is half of the greatest angle, we have:
A = (1/2)C
Substituting this value of A in the first equation, we get:
B = [(1/2)C + C]/2
B = (3/2)C/2
B = (3/4)C
Now, we know that the sum of the angles in a triangle is 180 degrees. So, we can write the equation:
A + B + C = 180
Substituting the values of A and B, we get:
(1/2)C + (3/4)C + C = 180
(4/8)C + (6/8)C + (8/8)C = 180
(18/8)C = 180
C = (8/18) * 180
C = 80 degrees
Using this value of C, we can find the other angles:
A = (1/2)C = (1/2) * 80 = 40 degrees
B = (3/4)C = (3/4) * 80 = 60 degrees
Therefore, the angles of the triangle are 40 degrees, 60 degrees, and 80 degrees.
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The angles of a triangle in A.P. the smallest being half of the greatest. So what are the angles ?a)45°, 55°, 90°b)50°, 25°, 75°c)60°, 40°, 80°d)40°, 60°, 30°Correct answer is 'C'. 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 The angles of a triangle in A.P. the smallest being half of the greatest. So what are the angles ?a)45°, 55°, 90°b)50°, 25°, 75°c)60°, 40°, 80°d)40°, 60°, 30°Correct answer is 'C'. 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 The angles of a triangle in A.P. the smallest being half of the greatest. So what are the angles ?a)45°, 55°, 90°b)50°, 25°, 75°c)60°, 40°, 80°d)40°, 60°, 30°Correct answer is 'C'. Can you explain this answer?.
The angles of a triangle in A.P. the smallest being half of the greatest. So what are the angles ?a)45°, 55°, 90°b)50°, 25°, 75°c)60°, 40°, 80°d)40°, 60°, 30°Correct answer is 'C'. 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 The angles of a triangle in A.P. the smallest being half of the greatest. So what are the angles ?a)45°, 55°, 90°b)50°, 25°, 75°c)60°, 40°, 80°d)40°, 60°, 30°Correct answer is 'C'. 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 The angles of a triangle in A.P. the smallest being half of the greatest. So what are the angles ?a)45°, 55°, 90°b)50°, 25°, 75°c)60°, 40°, 80°d)40°, 60°, 30°Correct answer is 'C'. Can you explain this answer?.
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