Angle B in isosceles trapezoid ABCD is 4 times the angle D. Find Angle A.

A trapezoid is a quadrilateral in which one pair of opposite sides is parallel, and the sides are not equal to each other.

Isosceles is a trapezoid in which the sides are equal:

AB = CD.

In an isosceles trapezoid, the angles at the bases are equal:

∠А = ∠D;

∠В = ∠С.

Since the sum of the angles adjacent to one side of the trapezoid is 180º, and the angle ∠В is four times greater than the angle ∠Д, then we express:

x – angle ∠D;

4x – angle ∠В;

x + 4x = 180;

5x = 180;

x = 180/5 = 36;

∠D = ∠A = 36º;

∠В = ∠С = 36 · 4 = 144º.

Answer: the degree measure of the angle ∠A is equal to 36º.