1. What is the Triangle Angle Sum Theorem?

The Triangle Angle Sum Theorem states that the sum of the interior angles of any triangle always equals 180 degrees. This fundamental geometric principle applies to all types of triangles (scalene, isosceles, equilateral, right, acute, and obtuse).

2. How Does the Calculator Work?

The calculator uses the simple formula:

Where:

• Angle1 — First interior angle (degrees)
• Angle2 — Second interior angle (degrees)
• Angle3 — Third interior angle (degrees)

Explanation: The calculator simply adds the three angle measurements you provide and displays the sum.

3. Importance of Angle Sum Calculation

Details: Verifying that angles sum to 180° helps confirm a shape is a triangle, check geometric constructions, and solve for missing angles in triangle problems.

4. Using the Calculator

Tips: Enter all three angle measurements in degrees. Each angle must be between 0 and 180 degrees, and the sum should be exactly 180° for a valid triangle.

5. Frequently Asked Questions (FAQ)

Q1: Does this theorem work for all triangles?
A: Yes, the sum of interior angles is always 180° for any triangle in Euclidean geometry.

Q2: What if my angles don't sum to 180°?
A: Either your measurements are inaccurate or the shape isn't a perfect triangle (possibly due to measurement error or non-Euclidean space).

Q3: Can I find a missing angle with this?
A: Yes, if you know two angles, subtract their sum from 180° to find the third angle.

Q4: Does this apply to polygons with more sides?
A: No, but similar theorems exist (e.g., quadrilateral angles sum to 360°). The general formula is (n-2)×180° for an n-sided polygon.

Q5: Why is this theorem important?
A: It's fundamental to geometry, used in proofs, constructions, and solving practical problems involving triangles.