In a cyclic quadrilateral, the opposite angles are related in which way? (2023)

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Question: In a cyclic quadrilateral, the opposite angles are related in which way? (2023)

Options:

Correct Answer: They are supplementary.

Exam Year: 2023

Solution:

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

In a cyclic quadrilateral, the opposite angles are related in which way? (2023)

In a cyclic quadrilateral, the opposite angles are related in which way? (2023)

Step 1: Understand what a cyclic quadrilateral is. It is a four-sided figure (quadrilateral) where all corners (vertices) lie on a single circle.
Step 2: Identify the opposite angles in the cyclic quadrilateral. These are the angles that are not next to each other.
Step 3: Learn about supplementary angles. Supplementary angles are two angles that add up to 180 degrees.
Step 4: Apply the property of cyclic quadrilaterals. In a cyclic quadrilateral, the opposite angles are always supplementary.
Step 5: Conclude that if you have two opposite angles in a cyclic quadrilateral, you can add them together, and their sum will equal 180 degrees.

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