1. What is the Inscribed Angle Formula for Triangles?

The inscribed angle formula for triangles relates the angles formed by two chords in a circle. For a triangle inscribed in a circle, the angle opposite to a side can be calculated from the other two angles.

2. How Does the Calculator Work?

The calculator uses the inscribed angle formula:

Where:

• \( a \) — First known angle (degrees)
• \( b \) — Second known angle (degrees)

Explanation: The formula calculates the third angle of a triangle inscribed in a circle based on the other two angles.

3. Importance of Inscribed Angles

Details: Understanding inscribed angles is crucial for solving geometric problems involving circles and triangles, particularly in trigonometry and circle geometry.

4. Using the Calculator

Tips: Enter both known angles in degrees. Values must be positive and their sum must be less than 360 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is an inscribed angle?
A: An inscribed angle is an angle formed by two chords in a circle that have a common endpoint on the circle.

Q2: Does this work for any triangle?
A: This formula specifically applies to triangles inscribed in a circle (cyclic triangles).

Q3: What's the relationship between inscribed angles and arcs?
A: The measure of an inscribed angle is half the measure of its intercepted arc.

Q4: Can I use this for right triangles?
A: Yes, the formula works for right triangles inscribed in a circle, where the hypotenuse is the diameter.

Q5: What if my angles add up to more than 180 degrees?
A: The calculator checks that the sum is valid (less than 360°). For a triangle, the sum of two angles should be less than 180°.