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In a quadrilateral, if one angle is 120 degrees and the other three angles are e

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Question: In a quadrilateral, if one angle is 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: 60 degrees

Solution: 

The sum of angles in a quadrilateral is 360 degrees. If one angle is 120 degrees, the remaining angles must sum to 240 degrees. Dividing this by 3 gives 80 degrees for each of the equal angles.

In a quadrilateral, if one angle is 120 degrees and the other three angles are e

Practice Questions

Q1
In a quadrilateral, if one angle is 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

In a quadrilateral, if one angle is 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 all angles in a quadrilateral is 360 degrees.
  • Step 3: Identify that one angle is given as 120 degrees.
  • Step 4: Subtract the 120 degrees from the total sum: 360 degrees - 120 degrees = 240 degrees.
  • Step 5: Recognize that the remaining three angles are equal, so we need to divide the 240 degrees by 3.
  • Step 6: Calculate the measure of each equal angle: 240 degrees ÷ 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 interior angles in any quadrilateral is always 360 degrees.
  • Equally Distributed Angles – When multiple angles are equal, their total can be found by dividing the remaining angle sum by the number of equal angles.
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