Answer
The angles are 38, 42 and 100.
Work Step by Step
Let X represent the smallest angle.
Three times the smallest means 3X.
14 less than three times the smallest angle means 3X - 14.
4 larger than the smallest angle means 4 + X
Thus, the angles are X, 3X - 14, and 4 + X
The sum of the angles in a triangle is 180, so we obtain:
X + 3X - 14 + 4 + X = 180
5X - 10 = 180
Add 10 to both sides.
5X = 190
Divide both sides by 5.
X = 38
Since X = 38, 3X - 14 = 100, and 4 +X = 42
The angles are 38, 42 and 100.
