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# If the length of the bases of an isosceles trapezoid are known can you compute the measure of the internal angles?

Updated: 11/4/2022

Wiki User

14y ago

Let's do an example.

Draw an isosceles trapezoid. Let say that the biggest base has a length of 10, and the smallest base has a length of 4.
Draw two perpendicular line that pass through the vertices of the smallest base, to the biggest base of the trapezoid.
A rectangle is formed whose lengths of its two opposite sides equal to the length of the smallest base of the trapezoid.
Then, we can say that the base of the right triangle whose hypotenuse is one one of the congruent sides of the trapezoid is 3, (1/2)(10 -4). So that one of the possibilities of its height (which also is the height of the trapezoid) is 4, and the hypotenuse is 5 (by the Pythagorean triple).
Now, in the right triangle whose hypotenuse is one of the congruent sides of the trapezoid, we have:
tan (base angle of the trapezoid) = 4/3, and
the base angle angle of the trapezoid = tan-1 (4/3) ≈ 53⁰.
Since the sum of the two adjacent angles of the trapezoid is 180⁰, the other angle of the trapezoid is 127⁰.
Thus, the base angles of the isosceles trapezoid have a measure of 53⁰, and two other angles have a measure of 127⁰.

So, we need to have more information in order to find the angles of the isosceles trapezoid for the given problem.

Wiki User

14y ago