In an isosceles trapezoid, the difference between the two angles is 15 degrees. Find the largest angle of this trapezoid.

Since the trapezoid ABCD is isosceles, its angles at the bases are equal, therefore, the difference between the two angles is the difference between the obtuse and acute angles at the lateral side of the trapezoid.

Angle (ABC – BAD) = 150. (1).

Since the sum of the angles of the trapezoid with its lateral side is 180, the angle (ABC + BAD) = 180. (2).

Let’s solve the system of two equations 1 and 2.

Let’s add both equations.

(ABC – BAD) + (ABC + BAD) = 15 + 180 = 195.

2 * ABC = 195.

Angle ABC = 195/2 = 97.5.

Answer: The largest angle of the trapezoid is 97.5.