Answer:
The three angles are 26°, 70° and 84°
Explanation:
Let the three angles be x, y and z respectively, and the sizes are ranging from x to y to z in ascending order.
Sum of angles in a triangle = 180°
In the question, it is given that
z = (x + y) - 12°
x = z - 58°
substitute the value for x into the expression for z
z = (z - 58° + y) - 12°
z = z + y - 70°
y = 70°
Recall
x + y + z = 180°
x + 70 + z = 180°
x + z = 110°
Recall
x = z - 58°
x - z = - 58
x + z = 110
Adding this two equations
2x = 52
x = 26°
x = z - 58
z = x + 58 = 26 + 58 = 84°
So, the three angles are 26°, 70° and 84°
