the measure of the largest angle of a triangle is 12 degrees less than the sum of the measures of the two. The smallest angle measures 58 degrees less than the largest. find the measure of the angles

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°