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The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral.
The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is
twice its smallest angle. What is the sum, in degrees, of the second largest angle of the
triangle and the largest angle of the quadrilateral?
The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is
twice its smallest angle. What is the sum, in degrees, of the second largest angle of the
triangle and the largest angle of the quadrilateral?
Correct answer is between '180,180'. Can you explain this answer?
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Verified Answer
The smallest angle of a triangle is equal to two thirds of the smalles...
Let the angles of quadrilateral are 3x, 4x, 5x, 6x
So, 3x+4x+5x+6x = 360
x = 20
Smallest angle of quadrilateral = 3×20 = 60°
Smallest angle of triangle = 2/3 x 60o = 40o
Largest angle of triangle = 2×40° = 60°
Three angles of triangle are 40°, 60°, 80°
Largest angle of quadrilateral is 120°
Sum (2nd largest angle of triangle + largest angle of quadrilateral)
= 60°+120°=180°.
So, 3x+4x+5x+6x = 360
x = 20
Smallest angle of quadrilateral = 3×20 = 60°
Smallest angle of triangle = 2/3 x 60o = 40o
Largest angle of triangle = 2×40° = 60°
Three angles of triangle are 40°, 60°, 80°
Largest angle of quadrilateral is 120°
Sum (2nd largest angle of triangle + largest angle of quadrilateral)
= 60°+120°=180°.
Most Upvoted Answer
The smallest angle of a triangle is equal to two thirds of the smalles...
Problem Analysis:
Solution:
- The problem is about finding angles of a triangle and a quadrilateral based on certain conditions.
- We are given that the smallest angle of the triangle is 2/3 of the smallest angle of the quadrilateral.
- We are also given the ratio of the angles of the quadrilateral.
- The largest angle of the triangle is twice its smallest angle.
- We need to find the sum of the second largest angle of the triangle and the largest angle of the quadrilateral.
Solution:
- Let the smallest angle of the triangle be x.
- Then, the largest angle of the triangle is 2x.
- Let the smallest angle of the quadrilateral be y.
- Then, according to the given condition, y = (3/2)x.
- Let the angles of the quadrilateral be 3a, 4a, 5a, and 6a.
- Therefore, the sum of the angles of the quadrilateral is 18a.
- Using the ratio of the angles, we can write:
- 3a + 4a + 5a + 6a = 18a
- 3x + 4x + 5x + 6x = 18y
- 18x = 18y
- x = y
- Therefore, we have x = y = (3/2)x.
- Substituting y = (3/2)x, we get:
- x = (3/2)x
- x = 60
- Therefore, the smallest angle of the triangle is 60 degrees.
- The largest angle of the triangle is twice the smallest angle, which is 120 degrees.
- The angles of the quadrilateral are:
- 3a = 180 - (60 + 80 + 100) = -60
- 4a = 240 - (60 + 80 + 100) = 0
- 5a = 300 - (60 + 80 + 100) = 60
- 6a = 360 - (60 + 80 + 100) = 120
- Since we cannot have negative angles, we add 360 to the negative angle.
- Therefore, the angles of the quadrilateral become:
- 3a = 300
- 4a = 360
- 5a = 60
- 6a = 120
- The largest angle of the quadrilateral is 6a, which is 120 degrees.
- The second largest angle of the triangle is 2x - x = x, which is 60 degrees.
- Therefore, the sum of the second largest angle of the triangle and the largest angle of the quadrilateral is:
- 60 + 120 = 180 degrees.
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The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral.The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle istwice its smallest angle. What is the sum, in degrees, of the second largest angle of thetriangle and the largest angle of the quadrilateral?Correct answer is between '180,180'. Can you explain this answer?
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The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral.The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle istwice its smallest angle. What is the sum, in degrees, of the second largest angle of thetriangle and the largest angle of the quadrilateral?Correct answer is between '180,180'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral.The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle istwice its smallest angle. What is the sum, in degrees, of the second largest angle of thetriangle and the largest angle of the quadrilateral?Correct answer is between '180,180'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral.The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle istwice its smallest angle. What is the sum, in degrees, of the second largest angle of thetriangle and the largest angle of the quadrilateral?Correct answer is between '180,180'. Can you explain this answer?.
The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral.The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle istwice its smallest angle. What is the sum, in degrees, of the second largest angle of thetriangle and the largest angle of the quadrilateral?Correct answer is between '180,180'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral.The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle istwice its smallest angle. What is the sum, in degrees, of the second largest angle of thetriangle and the largest angle of the quadrilateral?Correct answer is between '180,180'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral.The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle istwice its smallest angle. What is the sum, in degrees, of the second largest angle of thetriangle and the largest angle of the quadrilateral?Correct answer is between '180,180'. Can you explain this answer?.
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