The difference between the two angles of an isosceles trapezoid is 40 degrees. Find her corners.

The angles at the bases of an isosceles trapezoid are equal. Let us denote acute angles with a larger base of the trapezoid as x, and obtuse angles with a smaller base of the trapezoid as y.
By the theorem on the sum of the angles of a quadrangle:
x + y + y + x = 360 °;
2 * x + 2 * y = 360 ° (reduced by 2);
x + y = 180 °.
By condition, the difference between the two angles is 40 °. Since the angle y is obtuse, then its degree measure is greater than the degree measure of the x angle, then:
y – x = 40 °.
We got a system of linear equations with two unknowns:
x + y = 180 °;
y – x = 40 °.
In the first equation of the system, we express x through y:
x = 180 ° – y.
We substitute the resulting expression into the second equation of the system:
y – (180 ° – y) = 40 °;
y – 180 ° + y = 40 °;
2 * y = 40 ° + 180 °;
2 * y = 220 °;
y = 220 ° / 2;
y = 110 °.
Find the degree measure of the angle x:
x = 180 ° – y = 180 ° – 110 ° = 70 °.
Answer: the angles for the larger base are 70 °, the angles for the smaller base are 110 °.