BC and AD are the bases of the trapezoid. Angle A is 4 times smaller than angle B. What is angle B?

Since we know that ABCD is a trapezoid, then the angle A is equal to the angle D, and the angle B is equal to the angle C. It is also known that the sum of all the angles of the trapezoid is 360 °.

Let’s denote the angle A through the unknown x, then the angle B will be equal to 4 * x.

Thus, the following equation will be true:

x + 4 * x + 4 * x + x = 360 °;

x * (1 + 4 + 4 + 1) = 360 °;

x * 10 = 360 °;

x = 360 ° / 10;

x = 36 °.

Thus, we found the angle A and now we know that it is equal to 36 °.

This means that the angle B will be 4 * 36 ° = 144 °.

Answer: Angle B is 144 °.