Supplementary Angles Calculator
Find supplementary angles and check if two angles sum to 180° with step-by-step solutions
Calculate Supplementary Angles
Results
Calculation
Formula: Supplementary angle = 180° - given angle
Calculation: 180° - 0° = 180.0000°
Verification: 0° + 180.0000° = 180°
Trigonometric Relationships
Sine Values
sin(0°) = 0.0000
sin(180.00°) = 0.0000
✓ Equal values
Cosine Values
cos(0°) = 1.0000
cos(180.00°) = -1.0000
✓ Opposite signs
Tangent Values
tan(0°) = 0.0000
tan(180.00°) = -0.0000
✓ Opposite signs
Common Supplementary Angle Pairs
Example Calculations
Example 1: Find Supplementary Angle
Given: 65°
Formula: Supplementary angle = 180° - given angle
Calculation: 180° - 65° = 115°
Verification: 65° + 115° = 180° ✓
Example 2: Check if Supplementary
Given angles: 75° and 105°
Sum: 75° + 105° = 180°
Result: Yes, these angles are supplementary because their sum equals 180°
Supplementary Angles Properties
Sum to 180°
Two angles are supplementary if they add up to 180° (or π radians)
Linear Pair
Adjacent supplementary angles form a straight line
Angle Types
One acute + one obtuse, or both right angles
Trigonometric Properties
For supplementary angles α and β:
sin(α) = sin(β)
cos(α) = -cos(β)
tan(α) = -tan(β)
Where to Find Them
Linear pairs (adjacent angles on a line)
Consecutive angles in parallelograms
Co-interior angles with parallel lines
Same-side interior angles
Understanding Supplementary Angles
What are Supplementary Angles?
Supplementary angles are two angles whose measures add up to 180° (or π radians). The word "supplementary" comes from the Latin word "supplere," meaning "to complete" or "to make full."
Key Properties
- •Only two angles can be supplementary (not three or more)
- •Cannot both be obtuse or both be acute
- •Can be adjacent (forming a linear pair) or non-adjacent
- •Have special trigonometric relationships
How to Calculate
Finding a supplement:
Supplement = 180° - given angle
Supplement = π - given angle (radians)
Checking if supplementary:
angle₁ + angle₂ = 180° (or π rad)
If true, the angles are supplementary