Trapezoid Angle Calculator

Calculate all four angles of a trapezoid from its parallel sides and height or legs.

Select Input Method

Assumes an isosceles trapezoid (equal legs) unless offsets differ. For a general trapezoid, use Sides + Legs mode.

Trapezoid Angles

Sum of All Angles
360
degrees
Angle A (bottom-left)--
Angle B (bottom-right)--
Angle C (top-right)--
Angle D (top-left)--
Height--

Step-by-Step Solution

Co-interior angles sum to 180°

How Trapezoid Angles Work

In a trapezoid, the two bases are parallel. This means that each leg acts as a transversal cutting two parallel lines. By the co-interior angles theorem (also called consecutive interior angles or same-side interior angles), the angles on the same side of a leg are supplementary -- they add up to 180 degrees.

Angle Relationships

Co-Interior Angles

Angles between a base and a leg on the same side sum to 180 degrees.

A + D = 180°, B + C = 180°

Sum of All Angles

Like all quadrilaterals, the sum of all interior angles is 360 degrees.

A + B + C + D = 360°

Isosceles Trapezoid

Base angles are equal: A = B and C = D.

A = B, C = D

Finding Angles from Sides

Place the trapezoid in a coordinate system with the bottom base along the x-axis. The left bottom vertex is at the origin. Using the leg lengths and the difference of the bases, you can compute horizontal offsets and then use arctangent to find each base angle. The top angles are then 180 minus the corresponding base angle (co-interior property).

Method Using Height

  • For an isosceles trapezoid with height h and base difference (b - a), the horizontal offset on each side is (b - a) / 2.
  • Base angle = arctan(h / offset) = arctan(2h / (b - a)).
  • Top angle = 180 - base angle.