Trapezoid Angle Calculator

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.

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.

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,
$α = 55°$
then the tool determines,
$β = 125°$

and, if
$γ = 95°$
then
$δ = 85°$

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

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.

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

$\angle γ + \angle δ = \pi$

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:

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

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 (2π). You will get 105°.
3. This is the value of angle δ.

• Trapezoid calculator
• Area of a trapezoid calculator
• Trapezoid perimeter calculator
• Trapezoid side calculator
• Trapezoid height calculator
• Midsegment of a trapezoid
• Isosceles trapezoid calculator
• Isosceles trapezoid area calculator
• Right trapezoid calculator
• Right trapezoid area calculator
• Area of an irregular trapezoid calculator