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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?
    Correct answer is '180'. Can you explain this answer?
    Verified Answer
    The smallest angle of a triangle is equal to two thirds of the smalles...
    Let angle of quadrilateral be 3x, 4x, 5x, 6x
    Sum of angles of quadrilateral = 360 = 3x+4x+5x+6x = 18x
    x= 360/18 =20
    The smallest angle of triangle is ⅔ of smallest angle of quadrilateral = ⅔ (3x)
    = 2x = 40
    Largest angle of triangle is twice the smallest angle of triangle= 2x40 = 80
    Therefore, second largest angle of triangle = 180-Largest Angle- Smallest Angle
    = 180 - 80 -40 = 60
    Sum of second largest triangle and largest angle of quadrilateral = 60+ 6x
    = 60+ 6x20
    =180
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    Most Upvoted Answer
    The smallest angle of a triangle is equal to two thirds of the smalles...




    Given information:

    - Smallest angle of the triangle = 2/3 * Smallest angle of the quadrilateral
    - Ratio of angles in the quadrilateral = 3:4:5:6
    - Largest angle of the triangle = 2 * Smallest angle of the triangle



    Calculating angles:

    1. Let the smallest angle of the quadrilateral be 3x.
    2. Then the angles of the quadrilateral would be 3x, 4x, 5x, and 6x.
    3. Smallest angle of the triangle = 2/3 * 3x = 2x
    4. Largest angle of the triangle = 2 * 2x = 4x



    Calculating sum of angles:

    1. Second largest angle of the triangle = Largest angle of the triangle - Smallest angle of the triangle = 4x - 2x = 2x
    2. Largest angle of the quadrilateral = 6x

    Sum of the second largest angle of the triangle and the largest angle of the quadrilateral = 2x + 6x = 8x

    Given that the sum of the angles in both the triangle and the quadrilateral is 180 degrees, we have:

    2x + 4x + 2x + 3x + 4x + 5x + 6x = 180
    16x = 180
    x = 11.25

    Substitute x back into the angles:

    Second largest angle of the triangle = 2x = 22.5 degrees
    Largest angle of the quadrilateral = 6x = 67.5 degrees

    Sum of the second largest angle of the triangle and the largest angle of the quadrilateral = 22.5 + 67.5 = 90 degrees

    Therefore, the correct answer is 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 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 '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 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 '180'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) 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 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 '180'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 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 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 '180'. Can you explain this answer?.
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