In an isosceles trapezoid, the outer angle with a larger base is 96 degrees. Find the value of the angle

In an isosceles trapezoid, the outer angle with a larger base is 96 degrees. Find the value of the angle with a smaller base of the trapezoid.

1. It is known that:

a) in an isosceles trapezoid, the angles at the bases are equal;

b) the sum of adjacent angles is 180 *;

c) the sum of one-sided angles with parallel straight lines is 189 *.

2. The inner corner A of the trapezoid with a larger base is adjacent to the outer corner.

If, according to the condition of the problem, the outer angle is 96 *, then the inner angle is

angle A = 180 * – 96 * = 84 *.

3. The bases of the trapezoid are by definition parallel to each other, which means that the inner angle A of the trapezoid with a larger base is one-sided with an inner angle B of the trapezoid with a smaller base, and therefore they add up to 180 *.

Angle A + angle B = 180 *;

angle B = 180 * – angle A = 180 * – 84 * = 96 *.

Answer: The angle of the trapezoid with a smaller base is 96 *.

Find the inner corner of the trapezoid with a smaller base.