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

The formula ∠A = π - ∠C is derived from the fundamental property of cyclic quadrilaterals where opposite angles are supplementary. This means that the sum of opposite angles in a cyclic quadrilateral equals π radians (180 degrees).

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \angle A \) — Angle A of the cyclic quadrilateral (radians)
• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \angle C \) — Angle C of the cyclic quadrilateral (radians)

Explanation: This formula directly calculates angle A when angle C is known, based on the supplementary relationship between opposite angles in a cyclic quadrilateral.

3. Importance of Angle Calculation in Cyclic Quadrilaterals

Details: Understanding angle relationships in cyclic quadrilaterals is crucial for solving geometric problems, proving theorems, and applications in various fields including engineering, architecture, and computer graphics.

4. Using the Calculator

Tips: Enter angle C in radians (value must be ≥ 0). The calculator will compute angle A using the formula ∠A = π - ∠C.

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 angles in degrees?
A: The formula works with consistent units. For degrees, use ∠A = 180° - ∠C, but this calculator specifically uses radians.

Q4: What are the valid ranges for input angles?
A: Angle C should be between 0 and π radians (0° to 180°) for meaningful results in a cyclic quadrilateral.

Q5: Are there other angle relationships in cyclic quadrilaterals?
A: Yes, adjacent angles are also supplementary, and various other relationships exist based on specific cyclic quadrilateral properties.