1. What is the Angle C of Cyclic Quadrilateral Formula?

The formula calculates the measure of angle C in a cyclic quadrilateral using the measure of angle A. In a cyclic quadrilateral, opposite angles are supplementary, meaning they add up to π radians (180 degrees).

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \angle C \) — Angle C of Cyclic Quadrilateral (radians)
• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \angle A \) — Angle A of Cyclic Quadrilateral (radians)

Explanation: This formula is derived from the fundamental property of cyclic quadrilaterals where opposite angles are supplementary.

3. Importance of Angle Calculation

Details: Accurate angle calculation is crucial for geometric analysis, construction planning, and solving complex geometric problems involving cyclic quadrilaterals.

4. Using the Calculator

Tips: Enter angle A in radians. The value must be a positive number greater than 0 and less than π for meaningful results.

5. Frequently Asked Questions (FAQ)

Q1: What is a cyclic quadrilateral?
A: A cyclic quadrilateral is a four-sided polygon where all vertices lie on a single circle.

Q2: Why do opposite angles sum to π radians?
A: This is a fundamental property of cyclic quadrilaterals derived from the inscribed angle theorem in circle geometry.

Q3: Can this formula be used for degrees instead of radians?
A: Yes, but you would need to convert the formula to use 180 degrees instead of π radians.

Q4: What are the limitations of this formula?
A: This formula only applies to cyclic quadrilaterals and assumes the quadrilateral is properly inscribed in a circle.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, provided the input values are accurate and the quadrilateral is truly cyclic.