You are given a trapezoid ABCD isosceles (ab = cd). The diagonal AC is drawn

You are given a trapezoid ABCD isosceles (ab = cd). The diagonal AC is drawn, equal to the larger base AD. Angle B is 100 degrees. Find CAD corner.

In a trapezoid, the sum of the angles at the side is always 180 °, therefore:

angle A = 180 ° – angle B = 180 ° – 100 ° = 80 °;

Since trapezoid ABCD is isosceles, its lateral sides and lateral opposite angles are equal:

angle B = angle C = 100 °;

angle A = angle D = 80 °;

Since the AC diagonal = base of AD, the ACD triangle is isosceles:

angle D = angle ACD = 80 °;

Since the sum of the angles in any triangle is 180 °, according to its properties, we will find the CAD angle:

CAD angle = 180 ° – D angle – ACD angle = 180 ° – 80 ° – 80 ° = 20 °.