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
