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One of the angles of a triangle is half the larger angle of a parallelogram. The respective ratio between the adjacent angles of the parallelogram is 14 : 31 . The smallest angle of the triangle is half the smaller angle of the parallelogram. What is the value of the largest angle of the triangle?
- a)110°
- b)80°
- c)70°
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
One of the angles of a triangle is half the larger angle of a paralle...
We know that the sum of the adjacent angles of a parallelogram = 180o
View all questions of this test
Let the adjacent angles of the parallelogram be 14x and 31x
Therefore, 14x + 31x = 180o
45x = 180o
X = 4
Most Upvoted Answer
One of the angles of a triangle is half the larger angle of a paralle...
Given information:
- One angle of the triangle is half the larger angle of the parallelogram.
- The ratio between the adjacent angles of the parallelogram is 14:31.
- The smallest angle of the triangle is half the smaller angle of the parallelogram.
To find: The value of the largest angle of the triangle.
Let's assume the angles of the triangle as A, B, and C, and the angles of the parallelogram as X, Y, and Z.
Now, let's solve the problem step by step:
1. Relations between the angles of the parallelogram:
- X and Y are adjacent angles, and their ratio is given as 14:31.
2. Relations between the angles of the triangle and the parallelogram:
- One angle of the triangle is half the larger angle of the parallelogram. Let's assume angle A is half of angle Z.
- The smallest angle of the triangle is half the smaller angle of the parallelogram. Let's assume angle C is half of angle X.
3. Calculating the angles of the parallelogram:
- From the given ratio, let's assume the value of X as 14x and the value of Y as 31x.
- As angle A is half of angle Z, we can say that angle Z is 2A.
- Since angle X is smaller than angle Z, we can say that angle X is 2C.
- Therefore, angle X = 2C = 2(0.5A) = A.
4. Calculating the angles of the triangle:
- From the above relation, we have angle X = A.
- From the given information, we have angle C = 0.5X = 0.5A.
Now, let's calculate the value of the largest angle of the triangle:
- Sum of all angles of a triangle is 180 degrees.
- A + B + C = 180.
- A + B + 0.5A = 180.
- 1.5A + B = 180.
From the above equation, we can see that the value of angle B depends on the value of angle A. Since no specific value is given for angle A, we cannot determine the exact value of angle B or angle A.
Therefore, the correct answer is option 'D' - None of these.
- One angle of the triangle is half the larger angle of the parallelogram.
- The ratio between the adjacent angles of the parallelogram is 14:31.
- The smallest angle of the triangle is half the smaller angle of the parallelogram.
To find: The value of the largest angle of the triangle.
Let's assume the angles of the triangle as A, B, and C, and the angles of the parallelogram as X, Y, and Z.
Now, let's solve the problem step by step:
1. Relations between the angles of the parallelogram:
- X and Y are adjacent angles, and their ratio is given as 14:31.
2. Relations between the angles of the triangle and the parallelogram:
- One angle of the triangle is half the larger angle of the parallelogram. Let's assume angle A is half of angle Z.
- The smallest angle of the triangle is half the smaller angle of the parallelogram. Let's assume angle C is half of angle X.
3. Calculating the angles of the parallelogram:
- From the given ratio, let's assume the value of X as 14x and the value of Y as 31x.
- As angle A is half of angle Z, we can say that angle Z is 2A.
- Since angle X is smaller than angle Z, we can say that angle X is 2C.
- Therefore, angle X = 2C = 2(0.5A) = A.
4. Calculating the angles of the triangle:
- From the above relation, we have angle X = A.
- From the given information, we have angle C = 0.5X = 0.5A.
Now, let's calculate the value of the largest angle of the triangle:
- Sum of all angles of a triangle is 180 degrees.
- A + B + C = 180.
- A + B + 0.5A = 180.
- 1.5A + B = 180.
From the above equation, we can see that the value of angle B depends on the value of angle A. Since no specific value is given for angle A, we cannot determine the exact value of angle B or angle A.
Therefore, the correct answer is option 'D' - None of these.
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One of the angles of a triangle is half the larger angle of a parallelogram. The respective ratio between the adjacent angles of the parallelogram is 14 : 31 . The smallest angle of the triangle is half the smaller angle of the parallelogram. What is the value of the largest angle of the triangle?a)110°b)80°c)70°d)None of theseCorrect answer is option 'D'. Can you explain this answer?
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One of the angles of a triangle is half the larger angle of a parallelogram. The respective ratio between the adjacent angles of the parallelogram is 14 : 31 . The smallest angle of the triangle is half the smaller angle of the parallelogram. What is the value of the largest angle of the triangle?a)110°b)80°c)70°d)None of theseCorrect answer is option 'D'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about One of the angles of a triangle is half the larger angle of a parallelogram. The respective ratio between the adjacent angles of the parallelogram is 14 : 31 . The smallest angle of the triangle is half the smaller angle of the parallelogram. What is the value of the largest angle of the triangle?a)110°b)80°c)70°d)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for One of the angles of a triangle is half the larger angle of a parallelogram. The respective ratio between the adjacent angles of the parallelogram is 14 : 31 . The smallest angle of the triangle is half the smaller angle of the parallelogram. What is the value of the largest angle of the triangle?a)110°b)80°c)70°d)None of theseCorrect answer is option 'D'. Can you explain this answer?.
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