Interior & Exterior Triangle Angles Calculator
Calculate all interior and exterior angles of a triangle using angle sum theorem
Calculate Triangle Angles
Calculated automatically
Example Calculation
Right Triangle Example
Given: Angle A = 45°, Angle B = 90°
Calculate Angle C: C = 180° - 45° - 90° = 45°
Exterior Angles:
- Exterior at A = 180° - 45° = 135°
- Exterior at B = 180° - 90° = 90°
- Exterior at C = 180° - 45° = 135°
Verification: 135° + 90° + 135° = 360° ✓
Triangle Angle Theorems
Angle Sum Theorem
A + B + C = 180°
Exterior Angle Theorem
Exterior angle = sum of two opposite interior angles
Exterior Sum
Sum of all exterior angles = 360°
Triangle Types
Understanding Interior and Exterior Triangle Angles
Interior Angles
Interior angles are the angles inside a triangle. The most fundamental property of triangles is that the sum of all interior angles always equals 180° (or π radians). This is known as the Triangle Angle Sum Theorem.
Key Properties
- •Sum of interior angles = 180°
- •Each angle must be greater than 0° and less than 180°
- •If two angles are known, the third can be calculated
- •Angle measures determine triangle type
Exterior Angles
An exterior angle is formed when any side of a triangle is extended. Each vertex has two exterior angles that are equal to each other. The exterior angle equals the sum of the two opposite interior angles.
Exterior Angle Properties
- •Exterior angle = 180° - interior angle
- •Exterior angle = sum of two opposite interior angles
- •Sum of all exterior angles = 360°
- •Each triangle has 6 exterior angles (2 at each vertex)