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The largest and the second largest angles of a triangle are in the ratio of 3 : 2 respectively. The smallest angle is 20% of the sum of the rest two angles. What is the sum of the smallest and the second largest angles?
  • a)
    80°
  • b)
    60°
  • c)
    100°
  • d)
    90°
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The largest and the second largest angles of a triangle are in the ra...
If the largest and the second largest angles be 3x and 2x respectively then, third angle = x
∴ x + 2x + 3x = 180°
⇒ x = 30o
∴ Required sum
= x + 2x = 3x = 90°
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Most Upvoted Answer
The largest and the second largest angles of a triangle are in the ra...
Given information:
- The largest and the second largest angles of a triangle are in the ratio of 3:2.
- The smallest angle is 20% of the sum of the other two angles.

Let's assume:
- The largest angle = 3x
- The second largest angle = 2x

Finding the smallest angle:
- The sum of the largest and the second largest angles = 3x + 2x = 5x
- 20% of the sum of the other two angles = 0.2 * (3x + 2x) = 0.2 * 5x = x

Calculating the sum of all three angles:
- Sum of all three angles = smallest angle + largest angle + second largest angle
- Sum of all three angles = x + 3x + 2x = 6x

Calculating the value of x:
- From the given information, the smallest angle is 20% of the sum of the other two angles.
- Therefore, x = 0.2 * 5x
- Solving the equation, we get 1 = 0.2 * 5
- Thus, x = 1

Calculating the smallest and the second largest angles:
- Smallest angle = x = 1
- Second largest angle = 2x = 2 * 1 = 2

Calculating the sum of the smallest and the second largest angles:
- Sum of the smallest and the second largest angles = smallest angle + second largest angle
- Sum of the smallest and the second largest angles = 1 + 2 = 3

Therefore, the correct answer is option 'D' which is 90°.
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The largest and the second largest angles of a triangle are in the ratio of 3 : 2 respectively. The smallest angle is 20% of the sum of the rest two angles. What is the sum of the smallest and the second largest angles?a)80°b)60°c)100°d)90°Correct answer is option 'D'. Can you explain this answer?
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