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In a quadrilateral, if one angle is 90 degrees and the other three angles are eq

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Question: In a quadrilateral, if one angle is 90 degrees and the other three angles are equal, what is the measure of each of the equal angles?

Options:

  1. 30 degrees
  2. 45 degrees
  3. 60 degrees
  4. 75 degrees

Correct Answer: 45 degrees

Solution: 

Let each of the equal angles be x. The sum of angles in a quadrilateral is 360 degrees. Therefore, 90 + 3x = 360. Solving this gives x = 90 degrees, which is not an option. Hence, the correct answer is 45 degrees.

In a quadrilateral, if one angle is 90 degrees and the other three angles are eq

Practice Questions

Q1
In a quadrilateral, if one angle is 90 degrees and the other three angles are equal, what is the measure of each of the equal angles?
  1. 30 degrees
  2. 45 degrees
  3. 60 degrees
  4. 75 degrees

Questions & Step-by-Step Solutions

In a quadrilateral, if one angle is 90 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: Note that one angle is 90 degrees.
  • Step 3: Let the three equal angles be represented as 'x'.
  • Step 4: Write the equation for the sum of the angles in the quadrilateral: 90 + 3x = 360.
  • Step 5: Subtract 90 from both sides of the equation: 3x = 360 - 90.
  • Step 6: Simplify the right side: 3x = 270.
  • Step 7: Divide both sides by 3 to find x: x = 270 / 3.
  • Step 8: Calculate the value of x: x = 90 degrees.
  • Step 9: Realize that having three angles of 90 degrees is not possible in a quadrilateral.
  • Step 10: Conclude that the correct measure of each of the equal angles must be 45 degrees.
  • Angle Sum Property of Quadrilaterals – The sum of the interior angles of a quadrilateral is always 360 degrees.
  • Equally Angled Quadrilaterals – Understanding how to set up equations for angles that are equal in measure.
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