Angle Calculator
Understanding Angles
Types of Angles
- Acute Angle: < 90°
- Right Angle: = 90°
- Obtuse Angle: > 90° and < 180°
- Straight Angle: = 180°
- Reflex Angle: > 180° and < 360°
- Complete Angle: = 360°
Triangle Angle Properties
- Sum of angles = 180°
- Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
- Law of Cosines: c² = a² + b² - 2ab·cos(C)
- Exterior angle = sum of non-adjacent interior angles
- Altitude to hypotenuse divides right triangle into similar triangles
Polygon Angle Properties
Interior Angles
- Sum: (n-2) × 180°
- Regular polygon: (n-2) × 180°/n
Exterior Angles
- Sum: 360°
- Regular polygon: 360°/n
Central Angles
- Sum: 360°
- Regular polygon: 360°/n
Special Properties
- Regular polygons are equiangular
- Each exterior angle supplements its interior angle
- Central angle = 2 × inscribed angle
Advanced Angle Relationships
Complementary Angles
Two angles that sum to 90°
- sin(A) = cos(90° - A)
- cos(A) = sin(90° - A)
- tan(A) = cot(90° - A)
Supplementary Angles
Two angles that sum to 180°
- sin(A) = sin(180° - A)
- cos(A) = -cos(180° - A)
- tan(A) = -tan(180° - A)