1. What is Angle B of Cyclic Quadrilateral?

Angle B of Cyclic Quadrilateral is the space between the adjacent sides of Cyclic Quadrilateral, forming angle B. 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:

• \( \angle B \) — Angle B of Cyclic Quadrilateral (radians)
• \( \angle D \) — Angle D of Cyclic Quadrilateral (radians)
• \( \pi \) — Archimedes' constant (approximately 3.141592653589793)

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

3. Importance of Angle Calculation

Details: Calculating angles in cyclic quadrilaterals is essential for geometric analysis, construction planning, and solving problems in coordinate geometry and trigonometry.

4. Using the Calculator

Tips: Enter Angle D in radians. The value must be a non-negative number. The calculator will compute Angle B using the formula π - Angle D.

5. Frequently Asked Questions (FAQ)

Q1: What is a cyclic quadrilateral?
A: A cyclic quadrilateral is a four-sided polygon whose vertices all 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 radians. For degrees, use 180° instead of π (∠B = 180° - ∠D).

Q4: What are the constraints on angle values?
A: Both angles must be between 0 and π radians (0° and 180°) to form a valid cyclic quadrilateral.

Q5: Does this work for all cyclic quadrilaterals?
A: Yes, this property holds true for all cyclic quadrilaterals regardless of their specific shape or size.