Find the larger angle of the isosceles trapezoid ABCD if the diagonal AC makes angles equal

Find the larger angle of the isosceles trapezoid ABCD if the diagonal AC makes angles equal to 46 and 35 degrees with the base AD and the lateral side AB, respectively

The sum of the degree measures of the adjacent angles of the quadrangle is 180 degrees. Hence the angle ABC = 180- (BAC + CAD) = 180- (35 + 46) = 180-81 = 99. In an isosceles trapezoid, the angles at the base are equal, so the angle BCD = ABD = 99.
You can also consider the angles BAC and ABC as internal one-sided angles with parallel lines BC and AD and secant AB, which are 180 degrees in total.