In a quadrilateral, if one angle is 90 degrees and the opposite angle is 90 degr

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Question: In a quadrilateral, if one angle is 90 degrees and the opposite angle is 90 degrees, what can be concluded about the quadrilateral?

Options:

Correct Answer: It is a rectangle.

Solution:

If a quadrilateral has two opposite angles of 90 degrees, it must be a rectangle.

In a quadrilateral, if one angle is 90 degrees and the opposite angle is 90 degrees, what can be concluded about the quadrilateral?

In a quadrilateral, if one angle is 90 degrees and the opposite angle is 90 degrees, what can be concluded 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 in the quadrilateral. In this case, we have one angle that is 90 degrees and the opposite angle that is also 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 of 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: If the opposite angles are both 90 degrees, the other two angles must also be right angles (90 degrees each) to maintain the properties of a rectangle.
Step 7: Therefore, if a quadrilateral has two opposite angles of 90 degrees, it must be a rectangle.

Properties of Quadrilaterals – Understanding the properties of quadrilaterals, specifically how angles relate to the classification of shapes like rectangles.
Angle Relationships – Recognizing that having two opposite angles of 90 degrees indicates specific characteristics of the quadrilateral.