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

0.00°
Alpha (α)
0.00°
Beta (β)
0.00°
Gamma (γ)
0.00°
Delta (δ)

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