Let the constant difference between the angles be c

smallest angle = 75°
next to smallest angle = 75°+c
next to largest angle = 75°+c+c = 75°+2c
largest angle = 75°+2c+c = 75°+3c

The sum of the four angles of any quadrilateral is 360°

75° + (75°+c) + (75°+2c) + (75°+3c) = 360°
      75° + 75°+c + 75°+2c + 75°+3c = 360°
                          300° + 6c = 360°
                                 6c = 60°
                                  c = 30°

smallest angle = 75° 
next to smallest angle = 75°+c = 75°+30° = 105°
next to largest angle = 75°+2c = 75°+2(30°) = 75°+60° = 135° 
largest angle = 75°+2c+c = 75°+3c = 75°+3(30°) = 75°+90° = 165°

[Note:  You may point out to your teacher that this is a quadrilateral,
not a trapezium, because a trapezium has two parallel sides, and
therefore it must have two pairs of supplementary angles, and there 
is only one pair of supplementary angles, 75² and 105².  That's why
I changed the word "trapezium" to "quadrilateral".]

Edwin