One angle in a triangle has a measure that is three times as large as
the smallest angle. the measure of the third angle is 35 degrees more
than that of the smallest angle. find the measure of the largest angle

We know that the sum of all angles in any triangle is always 180 and we know that:

The smallest angle = x
Angle 2 = x + 35
Angle 3 = 3 * x

So:

180 = x + x + 35 + 3 * x
180 = x + x + 35 + 3x
180 = 2x + 35 + 3x
180 = 5x + 35                 / - 35 (both sides)
145 = 5x                         / ÷ 5 (both sides)
x = 29

The smallest angle = 29
Angle 2 = 29 + 35 = 64
Angle 3 = 3 * 29 = 87

Check:

29 + 64 + 87 = 180, so it's correct :)