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In a triangle, if the angles are in the ratio 2:3:4, what is the measure of the

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Question: In a triangle, if the angles are in the ratio 2:3:4, what is the measure of the largest angle? (2020)

Options:

  1. 60 degrees
  2. 80 degrees
  3. 90 degrees
  4. 120 degrees

Correct Answer: 120 degrees

Exam Year: 2020

Solution: 

Let the angles be 2x, 3x, and 4x. Then, 2x + 3x + 4x = 180, so 9x = 180, x = 20. The largest angle is 4x = 80 degrees.

In a triangle, if the angles are in the ratio 2:3:4, what is the measure of the

Practice Questions

Q1
In a triangle, if the angles are in the ratio 2:3:4, what is the measure of the largest angle? (2020)
  1. 60 degrees
  2. 80 degrees
  3. 90 degrees
  4. 120 degrees

Questions & Step-by-Step Solutions

In a triangle, if the angles are in the ratio 2:3:4, what is the measure of the largest angle? (2020)
  • Step 1: Understand that the angles of a triangle add up to 180 degrees.
  • Step 2: Let the angles be represented as 2x, 3x, and 4x based on the given ratio.
  • Step 3: Write an equation to represent the sum of the angles: 2x + 3x + 4x = 180.
  • Step 4: Combine the terms on the left side: 9x = 180.
  • Step 5: Solve for x by dividing both sides by 9: x = 20.
  • Step 6: Find the largest angle by calculating 4x: 4 * 20 = 80 degrees.
  • Angle Sum Property of Triangles – The sum of the interior angles of a triangle is always 180 degrees.
  • Ratios – Understanding how to work with ratios to express relationships between quantities.
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