Trapezoid Angle Calculator
Calculate all interior angles of a trapezoid using supplementary angle relationships
Calculate Trapezoid Angles
Choose angle measurement unit
Interior Angles
Calculated Angles
Validation
Total Sum: 0.00° ✗ (should be 360°)
Supplementary Pairs: ✗
α + β = 0.00°
γ + δ = 0.00°
Trapezoid Type
Type: Isosceles Trapezoid
Base Angles: Equal
Example: General Trapezoid
Given: α = 75°
Step 1: Find β using supplementary relationship
β = 180° - α = 180° - 75° = 105°
Step 2: For general trapezoid, γ and δ can vary
Step 3: Ensure γ + δ = 180° and total sum = 360°
Supplementary Angle Pairs
Adjacent angles are supplementary:
• α + β = 180° (angles along one leg)
• γ + δ = 180° (angles along other leg)
• Total: α + β + γ + δ = 360°
Trapezoid Properties
Total Angle Sum
α + β + γ + δ = 360°
Supplementary Pairs
α + β = 180°
γ + δ = 180°
Parallel Sides
One pair of opposite sides are parallel
Types of Trapezoids
General Trapezoid
No special angle relationships beyond supplementary pairs
Isosceles Trapezoid
Base angles are equal: α = δ and β = γ
Right Trapezoid
Has at least one right angle (90°)
Quick Tips
Adjacent angles are supplementary (sum to 180°)
All four angles sum to 360°
Know one angle? Find its adjacent partner easily
Right trapezoids have at least one 90° angle
Isosceles trapezoids have equal base angles
Understanding Trapezoid Angles
Angle Relationships
A trapezoid is a quadrilateral with one pair of parallel sides. This creates special relationships between the interior angles that help us calculate unknown angles.
α + β = 180°
γ + δ = 180°
Supplementary Pairs
- •Adjacent angles: Angles along the same leg are supplementary
- •Total sum: All four angles sum to 360°
- •Parallel sides: Create the supplementary relationship
Special Trapezoids
Isosceles Trapezoid
Base angles are equal: α = δ and β = γ
The legs are equal in length, creating symmetric angle pairs.
Right Trapezoid
Has at least one right angle (90°)
One leg is perpendicular to both parallel sides.
Applications
- •Architecture: Roof design and structural elements
- •Engineering: Bridge construction and mechanical parts
- •Geometry: Area and perimeter calculations