Question: In a cyclic quadrilateral, which of the following properties holds true?
Options:
The sum of opposite angles is 180 degrees.
All sides are equal.
It has at least one right angle.
The diagonals are equal.
Correct Answer: The sum of opposite angles is 180 degrees.
Solution:
In a cyclic quadrilateral, the sum of opposite angles is always 180 degrees.
In a cyclic quadrilateral, which of the following properties holds true?
Practice Questions
Q1
In a cyclic quadrilateral, which of the following properties holds true?
The sum of opposite angles is 180 degrees.
All sides are equal.
It has at least one right angle.
The diagonals are equal.
Questions & Step-by-Step Solutions
In a cyclic quadrilateral, which of the following properties holds true?
Step 1: Understand what a cyclic quadrilateral is. A cyclic quadrilateral is a four-sided figure (quadrilateral) where all the vertices lie on the circumference of a circle.
Step 2: Identify the angles in the cyclic quadrilateral. Label the angles as A, B, C, and D.
Step 3: Recognize the property of opposite angles. In a cyclic quadrilateral, the opposite angles are A and C, and B and D.
Step 4: Apply the property. The property states that the sum of the opposite angles is equal to 180 degrees. So, A + C = 180 degrees and B + D = 180 degrees.
Step 5: Conclude that this property holds true for all cyclic quadrilaterals.
Cyclic Quadrilateral Properties – In a cyclic quadrilateral, the sum of each pair of opposite angles is equal to 180 degrees.
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