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If a quadrilateral has one angle measuring 90 degrees and the opposite angle mea

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Question: If a quadrilateral has one angle measuring 90 degrees and the opposite angle measuring 90 degrees, what can be inferred about the quadrilateral?

Options:

  1. It is a trapezium.
  2. It is a rectangle.
  3. It is a rhombus.
  4. It is a kite.

Correct Answer: It is a rectangle.

Solution: 

A quadrilateral with two opposite angles measuring 90 degrees is a rectangle.

If a quadrilateral has one angle measuring 90 degrees and the opposite angle mea

Practice Questions

Q1
If a quadrilateral has one angle measuring 90 degrees and the opposite angle measuring 90 degrees, what can be inferred about the quadrilateral?
  1. It is a trapezium.
  2. It is a rectangle.
  3. It is a rhombus.
  4. It is a kite.

Questions & Step-by-Step Solutions

If a quadrilateral has one angle measuring 90 degrees and the opposite angle measuring 90 degrees, what can be inferred about the quadrilateral?
  • Step 1: Understand what a quadrilateral is. A quadrilateral is a shape with four sides and four angles.
  • Step 2: Identify the angles given in the question. We have one angle that measures 90 degrees and the opposite angle that also measures 90 degrees.
  • Step 3: Recall the properties of angles in a quadrilateral. The sum of all four angles in a quadrilateral is always 360 degrees.
  • Step 4: Since we have two angles that are 90 degrees, we can add them together: 90 + 90 = 180 degrees.
  • Step 5: This means that the other two angles must also add up to 180 degrees because 360 - 180 = 180.
  • Step 6: In a rectangle, opposite angles are equal, and adjacent angles are supplementary (they add up to 180 degrees).
  • Step 7: Since we have two opposite angles that are both 90 degrees, this confirms that the quadrilateral must be a rectangle.
  • Properties of Quadrilaterals – Understanding the characteristics of quadrilaterals, particularly the implications of having right angles.
  • Rectangles – Recognizing that a quadrilateral with two opposite right angles is a rectangle.
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