The measure of the three angles of the triangle cannot be determined based on the given information.
Let x be the measure of the smallest angle of the triangle.
According to the given information, the measure of the largest angle is equal to 3 times the sum of the measures of the other two angles:
Largest angle = 3(x + (180 - x - 4x))
Simplifying, we get:
Largest angle = 3(180 - 4x)
The sum of the measures of the smallest and largest angles is four times the measure of the remaining angle:
x + 3(180 - 4x) = 4(180 - x - 4x)
Simplifying further, we have:
x + 540 - 12x = 720 - 20x
540 - 720 = 20x - x - 12x
-180 = 7x
x = -180/7
Since the measure of an angle cannot be negative, this is not a valid solution. Therefore, there is no valid solution to this triangle.
Learn more about Triangle angles