Complementary Angles Calculator
Find complementary angles or check if two angles are complementary (sum to 90°)
Calculate Complementary Angles
The angle for which you want to find the complement
Results
Formula used: Complementary angle = 90° - angle (or π/2 - angle in radians)
Calculation: 90° - 0° = 0.0000°
Verification: 0° + 0.00° = 90°
Example Calculations
Finding a Complement
Given angle: 35°
Calculation: 90° - 35° = 55°
Result: The complementary angle is 55°
Verification: 35° + 55° = 90° ✓
Checking if Complementary
Angle 1: 30°
Angle 2: 60°
Sum: 30° + 60° = 90°
Result: Yes, they are complementary ✓
Right Triangle Example
In a right triangle: The two acute angles are always complementary
If one angle is 28°: The other must be 62°
Total: 28° + 62° + 90° = 180° (sum of triangle angles)
Quick Reference
Definition
Two angles are complementary if their sum equals 90° (π/2 radians)
Formula
Complement = 90° - angle
Or π/2 - angle (radians)
Common Examples
- • 30° + 60° = 90°
- • 45° + 45° = 90°
- • 25° + 65° = 90°
Trigonometric Relations
If α and β are complementary:
- • sin(α) = cos(β)
- • cos(α) = sin(β)
- • tan(α) = cot(β)
- • tan(α) × tan(β) = 1
Tips & Applications
In right triangles, the two acute angles are always complementary
45° is complementary to itself (45° + 45° = 90°)
Adjacent complementary angles form a right angle
Used in architecture, engineering, and navigation
Understanding Complementary Angles
What are Complementary Angles?
Complementary angles are two angles whose sum equals exactly 90° (or π/2 radians). This fundamental concept in geometry has wide applications in mathematics, engineering, and everyday problem-solving.
Key Properties
- •Sum always equals 90° (π/2 radians)
- •Can be adjacent or non-adjacent
- •Found in right triangles and rectangles
- •Have special trigonometric relationships
How to Find Complementary Angles
Complementary angle = 90° - given angle
or π/2 - given angle (in radians)
Real-World Applications
- Architecture: Roof angles and structural design
- Navigation: Bearing calculations and course corrections
- Engineering: Mechanical joint angles and stress analysis
- Art & Design: Perspective drawing and composition
Memory Tips
Visual Memory: Think of the letter "C" in complementary as looking like a 9, representing 90°.
Word Association: "Right to say compliments" - complementary angles form a right angle.