In a cyclic quadrilateral, which of the following statements is true?

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Question: In a cyclic quadrilateral, which of the following statements is true?

Options:

Correct Answer: The opposite angles are supplementary.

Solution:

In a cyclic quadrilateral, the opposite angles are supplementary, meaning they add up to 180 degrees.

In a cyclic quadrilateral, which of the following statements is true?

In a cyclic quadrilateral, which of the following statements is 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 a cyclic quadrilateral. There are four angles: angle A, angle B, angle C, and angle D.
Step 3: Learn about opposite angles. In a cyclic quadrilateral, the opposite angles are angle A and angle C, and angle B and angle D.
Step 4: Know the property of opposite angles in a cyclic quadrilateral. The property states that the sum of each pair of opposite angles is 180 degrees.
Step 5: Conclude that if you take angle A and angle C, their sum is 180 degrees. Similarly, angle B and angle D also add up to 180 degrees.

Cyclic Quadrilateral Properties – In a cyclic quadrilateral, the opposite angles are supplementary, meaning they add up to 180 degrees.