Trapezoid Angle Calculator

Created by Komal Rafay
Reviewed by Davide Borchia
Last updated: Mar 14, 2022

Are you looking for a trapezoid angle calculator? Because you have come to the right place. Our trapezoid angle calculator is a tool specially designed for all you geometry lovers. It determines the angles of a trapezoid: whether it is an isosceles or right-angle trapezoid, we have got you covered. Worry not, as we will explain how to calculate the angles of a trapezoid.

Angles of a trapezoid

There are four angles in a trapezoid:

  1. Alpha α;
  2. Beta β;
  3. Gamma γ; and
  4. Delta δ.

Like all other quadrangles, the sum of angles in a trapezoid is 360 degrees (or 2π radians).
Since they have a pair of parallel sides, the trapezoid has an additional condition. The pair of angles along one of the legs are supplementary angles, which means their sum must be equal to 180 degrees (or π radians).
It looks like this:

α + β = 𝛾+ δ = 180°

Knowing the angles of a trapezoid comes in handy to identify its height, and the height helps identify the area of trapezoid.

Trapezoid angle calculator

Our trapezoid angle calculator is a convenient tool that lets you calculate the different angles between the sides of the trapezoid.
You may input the value of any angle and obtain the value of its supplementary partner. Yes, it is really that simple.

For instance,
if you input,
α=55°α = 55°
then the tool determines,
β=125°β = 125°

and, if
γ=95°γ = 95°
then
δ=85°δ = 85°

In the tool, you can also select a different unit for angle conversion.

Types of a trapezoid

Now would be a good time to discuss the two most essential trapezoid types in terms of the angles.

  • Angle of isosceles trapezoid
    A trapezoid in which the legs and both of the base angles are of equal measure is an isosceles trapezoid. The angles of isosceles trapezoids are independent of the shape and are calculated the same way as a regular trapezoid.

  • Angle of right trapezoid
    A trapezoid whose one leg is perpendicular to the bases is a right trapezoid. It has at least one right angle.

🙋 Interestingly, if one of the legs is perpendicular to one of the bases, it is perpendicular to the other since the legs are parallel. So, chances are your right trapezoid has two right angles.

How to calculate angles of a trapezoid?

By now, we understand that the angles are supplementary and can calculate them in pairs.
The formula is:
α+β=π\angle α +\angle β = \pi

γ+δ=π\angle γ + \angle δ = \pi

Let's consider an example, you have ∠α = 75°, then to determine ∠β, subtract 75 from 180, and you have 105°.

The formula to calculate all four angles together is:

α+β+γ+δ=2π\angle α + \angle β + \angle γ + \angle δ = 2\pi

For instance, α = 75°, β =85°, and γ = 95°. To determine δ, follow the steps:

  1. Sum the values of α, β, and 𝛾. You will obtain 255°
  2. Next, subtract the summed value from 360 (). You will get 105°.
  3. This is the value of angle δ.

FAQ

What is the 4ᵗʰ angle of a right trapezoid, if first angle is 85°?

The value of the fourth angle is 95°.
A right trapezoid means a pair of its angles is 90°. This makes it easier to determine the angles. If two of the angles are 90° and 90°, and you know the third angle, you may subtract the value of the third angle from 180°.

How do I calculate the angles of a trapezoid?

To calculate the supplementary angles in pairs, the formula is:

∠α + ∠β = π

∠γ + ∠δ = π

where:

  • π = 180°.

So, if you have α = 100°, then β is obtained by subtracting 100° from 180°, which gives β = 80°.
The same procedure is valid for the pair of angles γ and δ.

If α = 75°, how much is β?

If α = 75°, then β =105°.
Although a trapezoid is a quadrangle shape and the sum of its angles is 360°. There is a condition for trapezoid that the pair of angles along one of the legs are supplementary angles, which means their sum must be equal to 180 degrees.
So, you can determine one angle by knowing its adjacent partner.

Komal Rafay
A trapezoid with sides, angles and height marked
α
deg
β
deg
γ
deg
δ
deg
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