Final answer:
To find the ratio of the angles from smallest to biggest, the middle and smallest angles were calculated using the sum of the angles in the triangle and the given conditions. The ratio was found to be 3:4:5.
Step-by-step explanation:
Given that the largest angle in a triangle is 75°, and the difference between the two other angles is 15°, we know that the sum of the angles in a triangle is 180°. Let's denote the middle angle as x degrees, then the smallest angle will be x - 15° and the sum of the angles can be written as:
(x) + (x - 15°) + (75°) = 180°
Simplifying, we get:
2x + 60° = 180°
2x = 120°
x = 60°
Therfore, the smallest angle is 60° - 15° = 45°.
The ratio of the angles from smallest to largest is 45:60:75. This simplifies to 3:4:5 because each term is divisible by 15.