In an isosceles triangle, the angle at the base is 4 times the angle between the lateral sides. Find the corners of the triangle.

Angle B is the angle between the lateral sides of an isosceles triangle.
In any triangle, the sum of all three angles is 180 degrees (the theorem on the sum of the angles of a triangle). In this way:
angle A + angle B + angle C = 180 degrees.
Let x be the coefficient of proportionality, then angle A = 4x, and angle B = x, since angle A is 4 times greater than angle B. Since triangle ABC is isosceles, and angle B is the angle between the sides, then angles A and C are equal, since they are angles at the base. Then angle A = angle C = 4x.
4x + x + 4x = 180 degrees;
9x = 180 degrees;
x = 180 degrees / 9;
x = 20 degrees.
It turns out that angle B = x = 20 degrees, angle A = angle C = 4x = 4 * 20 degrees = 80 degrees.
Answer: angle A = 80 degrees, angle B = 20 degrees, angle C = 80 degrees.