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The ratio between the angles of a quadrilateral is 6 : 3 : 4 : 5. The smallest angle of a triange is one-fourth the largest angle of the quadrilateral. Largest angle of the triangle is 10° more than second largest angle of the triangle. What is the second largest angle of the triangle? 
 
  • a)
    80°
  • b)
    60°
  • c)
    70°
  • d)
    Cannot be determined
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The ratio between the angles of a quadrilateral is 6 : 3 : 4 : 5. The ...
Option C
The largest angle of the quadrilateral =   = 120°
The smallest angle of the triangle = 120 ×(1/4) = 30°
If the second largest angle of the triangle be x°, then the largest angle of the triangle = (x° + 10°)
30 + x + x + 10 = 180 x = 70°
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Most Upvoted Answer
The ratio between the angles of a quadrilateral is 6 : 3 : 4 : 5. The ...
Given data:
Ratio of angles of quadrilateral = 6 : 3 : 4 : 5
Let the angles of the quadrilateral be 6x, 3x, 4x and 5x respectively.
Also, the smallest angle of the triangle = (1/4) × largest angle of the quadrilateral = (1/4) × 5x = (5/4)x
Let the angles of the triangle be a, b and c such that a ≤ b ≤ c.
Also, c = 10 + b.
We need to find the value of b.
Approach:
The sum of angles of a quadrilateral is 360°.
Hence, we can find the value of x and the angles of the quadrilateral.
Using the given information, we can also find the value of (5/4)x.
Further, we can use the fact that the sum of angles of a triangle is 180° to find the value of c and hence, b.
Calculation:
Let us first find the value of x.
6x + 3x + 4x + 5x = 360°
18x = 360°
x = 20°
Hence, the angles of the quadrilateral are:
6x = 120°
3x = 60°
4x = 80°
5x = 100°
Smallest angle of the triangle = (5/4)x = (5/4) × 20° = 25°
Let us denote the angles of the triangle as a, b and c such that a ≤ b ≤ c.
Also, c = 10 + b.
a + b + c = 180°
a + b + (b + 10) = 180°
2b + 10 + a = 180°
a + 2b = 170°
Since a ≤ b ≤ c, we have:
a + b > c
a + b > b + 10
a > 10
Hence, the possible values of a and b are:
a = 11°, b = 79.5°, c = 89.5°
a = 12°, b = 79°, c = 89°
a = 13°, b = 78.5°, c = 88.5°
a = 14°, b = 78°, c = 88°
...
a = 78°, b = 46°, c = 56°
a = 79°, b = 45.5°, c = 55.5°
a = 80°, b = 45°, c = 55°
Since the largest angle of the triangle is 80°, the second largest angle is 45°.
Hence, the correct answer is option (c) 70.
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Community Answer
The ratio between the angles of a quadrilateral is 6 : 3 : 4 : 5. The ...
Answer ( C )
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The ratio between the angles of a quadrilateral is 6 : 3 : 4 : 5. The smallest angle of a triange is one-fourth the largest angle of the quadrilateral. Largest angle of the triangle is 10° more than second largest angle of the triangle. What is the second largest angle of the triangle?a)80°b)60°c)70°d)Cannot be determinede)None of theseCorrect answer is option 'C'. Can you explain this answer?
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The ratio between the angles of a quadrilateral is 6 : 3 : 4 : 5. The smallest angle of a triange is one-fourth the largest angle of the quadrilateral. Largest angle of the triangle is 10° more than second largest angle of the triangle. What is the second largest angle of the triangle?a)80°b)60°c)70°d)Cannot be determinede)None of theseCorrect answer is option 'C'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about The ratio between the angles of a quadrilateral is 6 : 3 : 4 : 5. The smallest angle of a triange is one-fourth the largest angle of the quadrilateral. Largest angle of the triangle is 10° more than second largest angle of the triangle. What is the second largest angle of the triangle?a)80°b)60°c)70°d)Cannot be determinede)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio between the angles of a quadrilateral is 6 : 3 : 4 : 5. The smallest angle of a triange is one-fourth the largest angle of the quadrilateral. Largest angle of the triangle is 10° more than second largest angle of the triangle. What is the second largest angle of the triangle?a)80°b)60°c)70°d)Cannot be determinede)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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