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  1. Asked: March 27, 2026In:

    The measures of the three angles of a triangle are in the ratio 17 : 13 : 15. Find the positive difference between the greatest and the smallest of these three angles.

    Content Team
    Content Team

    The measures of the three angles of a triangle are in the ratio 17 : 13 : 15. Formula Used: Sum of angles in a triangle = 180º Let the measures of the three angles be 17x, 13x, and 15x. Calculation: Sum of the angles = 17x + 13x + 15x 17x + 13x + 15x = 180º ⇒ 45x = 180º ⇒ x = 180º / 45 ⇒ x = 4º TheRead more

    The measures of the three angles of a triangle are in the ratio 17 : 13 : 15.

    Formula Used:

    Sum of angles in a triangle = 180º

    Let the measures of the three angles be 17x, 13x, and 15x.

    Calculation:

    Sum of the angles = 17x + 13x + 15x

    17x + 13x + 15x = 180º

    ⇒ 45x = 180º

    ⇒ x = 180º / 45

    ⇒ x = 4º

    The greatest angle = 17x = 17 × 4º = 68º

    The smallest angle = 13x = 13 × 4º = 52º

    The positive difference between the greatest and the smallest angle = 68º – 52º = 16º

    The correct answer is option 1.

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  2. Asked: March 25, 2026

    The average of 12 numbers is 48. The average of the first 5 numbers is 45, and the average of the next 4 numbers is 52. If the 10th number is 10 less than the 11th number and is 5 more than the 12th number, then the average of the 11th and 12th numbers is:

    Content Team
    Content Team
    This answer was edited.

    Given: Average of 12 numbers = 48 Average of first 5 numbers = 45 Average of next 4 numbers = 52 10th number = 11th number - 10 10th number = 12th number + 5 Formula used: Sum = Average × Number of terms Calculations: Total sum of 12 numbers = 48 × 12 = 576 Sum of first 5 numbers = 45 × 5 = 225 SumRead more

    Given:

    Average of 12 numbers = 48

    Average of first 5 numbers = 45

    Average of next 4 numbers = 52

    10th number = 11th number – 10

    10th number = 12th number + 5

    Formula used:

    Sum = Average × Number of terms

    Calculations:

    Total sum of 12 numbers = 48 × 12 = 576

    Sum of first 5 numbers = 45 × 5 = 225

    Sum of next 4 numbers = 52 × 4 = 208

    Sum of 10th, 11th, and 12th numbers = 576 – (225 + 208) = 143

    Let the 11th number = x.

    Then, 10th number = x – 10 and 12th number = x – 15.

    Sum of 10th, 11th, and 12th numbers:

    (x – 10) + x + (x – 15) = 143

    ⇒ 3x – 25 = 143

    ⇒ 3x = 168

    ⇒ x = 56

    11th number = 56

    12th number = 56 – 15 = 41

    Average of 11th and 12th numbers = (56 + 41) ÷ 2 = 48.5

    ∴ The average of the 11th and 12th numbers is 48.5.

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