Find the angles of an isosceles trapezoid ABCD with a large base AD if the angle C is the angle A = 80 degrees.

Given:
isosceles trapezoid ABCD,
AD – larger base,
angle C – angle A = 80 degrees.
Find the angles of an isosceles trapezoid ABCD: angle A, angle A, angle B, angle C, angle D -?
Decision:
Consider an isosceles trapezoid ABCD. Its adjacent angles at the base are equal to each other, then angle A = angle D, angle B = angle C.
Let the degree measure of angle A be equal to x degrees, then the degree measure of angle C is equal to 80 + x degrees. We know that the sum of the degree measures of a parallelogram is 360 degrees. Let’s make the equation:
x + x + x + 80 + x + 80 = 360;
x + x + x + x + 160 = 360;
x + x + x + x = 360 – 160;
x + x + x + x = 200;
x * (1 + 1 + 1 + 1) = 200;
x * 4 = 200;
x = 200: 4;
x = 50 degrees – the degree measure of angle A and angle D;
50 + 80 = 130 degrees – the degree measure of angle C and angle B.
Answer: 50 degrees; 130 degrees; 130 degrees; 50 degrees.