# In an isosceles trapezoid ABCD, the angle between the diagonal AC

In an isosceles trapezoid ABCD, the angle between the diagonal AC and the base AB is 40 degrees and AD = DC. Find the corners of the trapezoid

Angle DCA = CAB = 40 as intersecting angles at the intersection of parallel straight lines DC and AB secant AC.

Since, according to the condition, AD = DC, then the triangle ADC is isosceles, which means the angle DAC = DCA = 40.

Then the angle DАВ = DАС + BAC = 40 + 40 = 80.

Since the sum of the angles at the lateral sides of the trapezoid is 180, the angle ADC = 180 – 80 = 100.

Angle DCB = ADC = 100, angle ABC = DAB = 80, since the angles at the bases are equal.

Answer: The angles of the trapezoid are 80, 100, 80, 100. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.