Trapezoid Angle Calculator — Base & Top Interior Angles
Given the top base, bottom base, and equal leg of an isosceles trapezoid, compute the base angle (α) and top angle (β = 180° − α), and the perpendicular height.
Interior angle at each bottom corner — both are equal in an isosceles trapezoid
- 1
Half base difference (leg projection)
(10 − 6) ÷ 2 = 2 - 2
Perpendicular height (Pythagorean theorem)
√(5² − 2²) = √21 = 4.5826 - 3
Base angle α = arctan(h / offset)
arctan(4.5826 ÷ 2) = 66.4218
How does this calculator work?
For an isosceles trapezoid with bases a (top) and b (bottom) and leg c: height h = √(c²−((b−a)/2)²), base angle α = arctan(h/((b−a)/2)), top angle β = 180°−α. Co-interior angles are supplementary; all four angles sum to 360°.
Formula
How this is calculated
In an isosceles trapezoid the two non-parallel sides (legs) are equal in length. Dropping a perpendicular from each top corner to the bottom base creates two congruent right triangles on the sides, each with hypotenuse c (the leg) and base (b−a)/2. The height of the trapezoid is h = √(c² − ((b−a)/2)²) by the Pythagorean theorem.
The base angle α — the interior angle at each bottom corner — equals arctan(h / ((b−a)/2)), or equivalently arccos((b−a)/(2c)). Because the two bases are parallel, the co-interior angles on the same leg are supplementary: α + β = 180°, so the top angle β = 180° − α. All four angles sum to 360°: two base angles and two top angles.
The formula requires the leg to be strictly longer than (b−a)/2 — otherwise the trapezoid is degenerate (height would be zero or imaginary). When b = a the shape is a rectangle and both angles are 90°.
Frequently asked questions
Because the two bases are parallel, the leg acts as a transversal. Co-interior angles (same-side interior angles) formed between a transversal and two parallel lines are always supplementary — they sum to 180°.
No — for a scalene trapezoid you need to know both leg lengths and use a four-variable coordinate system. This calculator assumes both legs are equal (isosceles trapezoid), which is the most common case in geometry problems.
Rearrange: if you know α and the bottom base b and top base a, the leg is c = (b−a)/(2 cos α) and the height is h = (b−a) tan(α) / 2. Most geometry textbooks present the forward direction (sides → angles) as covered here.
Also known as
TG we-Calculate Editorial Team. (2026). Trapezoid Angle Calculator — Base & Top Interior Angles [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/trapezoid-angle-calculator
TG we-Calculate Editorial Team. "Trapezoid Angle Calculator — Base & Top Interior Angles." TG we-Calculate. 2026. https://we-calculate.com/calculator/trapezoid-angle-calculator.
TG we-Calculate Editorial Team, "Trapezoid Angle Calculator — Base & Top Interior Angles," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/trapezoid-angle-calculator
@misc{wecalculate_trapezoid_angle_calculator, title = {Trapezoid Angle Calculator — Base & Top Interior Angles}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/trapezoid-angle-calculator}}, year = {2026}, note = {TG we-Calculate} }
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