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If the angles of a quadrilateral are in the ratio 1:2:3:4, what is the measure o

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Question: If the angles of a quadrilateral are in the ratio 1:2:3:4, what is the measure of the largest angle?

Options:

  1. 90 degrees
  2. 120 degrees
  3. 150 degrees
  4. 180 degrees

Correct Answer: 150 degrees

Solution: 

Let the angles be x, 2x, 3x, and 4x. The sum of angles in a quadrilateral is 360 degrees. Therefore, x + 2x + 3x + 4x = 360, which gives 10x = 360, so x = 36 degrees. The largest angle = 4x = 144 degrees.

If the angles of a quadrilateral are in the ratio 1:2:3:4, what is the measure o

Practice Questions

Q1
If the angles of a quadrilateral are in the ratio 1:2:3:4, what is the measure of the largest angle?
  1. 90 degrees
  2. 120 degrees
  3. 150 degrees
  4. 180 degrees

Questions & Step-by-Step Solutions

If the angles of a quadrilateral are in the ratio 1:2:3:4, what is the measure of the largest angle?
  • Step 1: Understand that a quadrilateral has four angles.
  • Step 2: Let the angles be represented as x, 2x, 3x, and 4x based on the given ratio of 1:2:3:4.
  • Step 3: Write down the equation for the sum of the angles in a quadrilateral: x + 2x + 3x + 4x = 360 degrees.
  • Step 4: Combine the terms on the left side: 1x + 2x + 3x + 4x = 10x.
  • Step 5: Set up the equation: 10x = 360 degrees.
  • Step 6: Solve for x by dividing both sides by 10: x = 36 degrees.
  • Step 7: Find the largest angle by calculating 4x: 4 * 36 = 144 degrees.
  • Step 8: Conclude that the measure of the largest angle is 144 degrees.
  • Angle Sum Property of Quadrilaterals – The sum of the interior angles of a quadrilateral is always 360 degrees.
  • Ratios – Understanding how to express quantities in terms of ratios and solve for unknowns.
  • Algebraic Manipulation – Using algebra to solve equations derived from geometric properties.
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