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

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Question: If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?

Options:

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

Correct Answer: 80 degrees

Solution: 

Let the angles be 2x, 3x, and 4x. The sum of angles in a triangle is 180 degrees. Therefore, 2x + 3x + 4x = 180. Solving gives x = 20, so the largest angle is 4x = 80 degrees.

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

Practice Questions

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

Questions & Step-by-Step Solutions

If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?
  • Step 1: Understand that the angles of the triangle are in the ratio 2:3:4. This means we can represent the angles as 2x, 3x, and 4x, where x is a common multiplier.
  • Step 2: Write down the equation for the sum of the angles in a triangle. The sum of the angles in any triangle is always 180 degrees.
  • Step 3: Set up the equation: 2x + 3x + 4x = 180.
  • Step 4: Combine the terms on the left side of the equation: (2x + 3x + 4x) = 9x, so the equation becomes 9x = 180.
  • Step 5: Solve for x by dividing both sides of the equation by 9: x = 180 / 9.
  • Step 6: Calculate x: x = 20.
  • Step 7: Now, find the largest angle, which is represented by 4x. Multiply 4 by the value of x: 4x = 4 * 20.
  • Step 8: Calculate 4x: 4x = 80 degrees. This is the measure of the largest angle.
  • Triangle Angle Sum – The sum of the interior angles of a triangle is always 180 degrees.
  • Ratio and Proportion – Understanding how to express quantities in a given ratio and solve for unknowns.
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