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If a quadrilateral has one angle measuring 120 degrees and the other three angle

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Question: If a quadrilateral has one angle measuring 120 degrees and the other three angles are equal, what is the measure of each of the equal angles?

Options:

  1. 30 degrees
  2. 40 degrees
  3. 60 degrees
  4. 80 degrees

Correct Answer: 40 degrees

Solution: 

The sum of the angles in a quadrilateral is 360 degrees. If one angle is 120 degrees, the remaining angles must sum to 240 degrees. If the other three angles are equal, each must be 240/3 = 80 degrees.

If a quadrilateral has one angle measuring 120 degrees and the other three angle

Practice Questions

Q1
If a quadrilateral has one angle measuring 120 degrees and the other three angles are equal, what is the measure of each of the equal angles?
  1. 30 degrees
  2. 40 degrees
  3. 60 degrees
  4. 80 degrees

Questions & Step-by-Step Solutions

If a quadrilateral has one angle measuring 120 degrees and the other three angles are equal, what is the measure of each of the equal angles?
  • Step 1: Understand that a quadrilateral has four angles.
  • Step 2: Know that the total sum of the angles in a quadrilateral is 360 degrees.
  • Step 3: Identify that one angle measures 120 degrees.
  • Step 4: Subtract the 120 degrees from the total sum: 360 - 120 = 240 degrees.
  • Step 5: Recognize that the remaining three angles must add up to 240 degrees.
  • Step 6: Since the three remaining angles are equal, divide 240 degrees by 3: 240 / 3 = 80 degrees.
  • Step 7: Conclude that each of the equal angles measures 80 degrees.
  • Sum of Angles in a Quadrilateral – The total measure of the interior angles in any quadrilateral is always 360 degrees.
  • Equally Distributed Angles – When multiple angles are equal, their individual measures can be found by dividing the total measure of those angles by the number of angles.
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