The measure of the largest angle of a certain triangle is 6 times the smallest. The measure of the remaining angle is 100 degrees less than te sum of the other two angles. Write a system of 3 equations you could use to solve this problem. x=smallest y=other angle z=largest

The measure of the largest angle of a certain triangle is 6 times the smallest. The measure of the remaining angle is 100 degrees less than te sum of the other two angles. Write a system of 3 equations you could use to solve this problem. x=smallest y=other angle z=largest

z = 6x
y = x + z - 100
x + y + z = 180

To solve this problem, we need to translate the given information into mathematical equations. Let's denote the smallest angle by 'x,' the other angle by 'y,' and the largest angle by 'z.'

1. The measure of the largest angle is 6 times the smallest angle:
z = 6x

2. The measure of the remaining angle is 100 degrees less than the sum of the other two angles:
y = (x + z) - 100

3. The sum of all three angles in a triangle is always 180 degrees:
x + y + z = 180

So, the system of equations is:
z = 6x
y = (x + z) - 100
x + y + z = 180

You can now solve this system of equations to find the values of x, y, and z, which represent the measures of the angles in the triangle.