Find the larger angle of the isosceles trapezoid ABCD if the diagonal AC

Find the larger angle of the isosceles trapezoid ABCD if the diagonal AC makes angles of 12 degrees and 13 degrees with the base AD and the lateral side AB, respectively.

Initially, we need to find the angle BAD, as the sum of the angles that form the AC diagonal with the side and the base:
∠BAD = ∠BAC + ∠CAD = 12 + 13 = 25 degrees.
Now we can use one of the main properties of an isosceles trapezoid, namely, that the sum of the angles that adjoin one side is 180 degrees, we find the angle ABC:
∠ABS = 180 – ∠BAD = 180 – 25 = 155 degrees.
Answer: the greater angle of this trapezoid is 155 degrees.