Find the angle acd of an isosceles trapezoid ABCD if the diagonal AC forms an angle of 35 degrees

Find the angle acd of an isosceles trapezoid ABCD if the diagonal AC forms an angle of 35 degrees with the base AD, and the major angle (B) of the trapezoid is 130

It is known that in a trapezoid the sum of the angles adjacent to the lateral side is 180 °. If the angle B = 130 °, then the angle A = 180 ° – 130 ° = 50 °.

Since this trapezoid is isosceles, the angles at the bases are equal to each other, which means the angles A and D are equal, therefore the angle D is also 50 °.

In triangle ACD, the angles D and CAD are known to be 50 ° and 35 °, respectively. The sum of the angles of the triangle is 180 °, so the angle ACD = 180 ° – 50 ° – 35 ° = 95 °.