In a triangle with angles (3x - 5), (2x + 3), and (x + 2), what is the measure of the largest angle in degrees?

To find the measure of the largest angle in the triangle with angles expressed as (3x - 5), (2x + 3), and (x + 2), we first need to use the fact that the sum of the angles in any triangle is always 180 degrees.

Start by writing the equation representing the sum of the angles:

(3x - 5) + (2x + 3) + (x + 2) = 180.

Now, combine like terms:

3x + 2x + x - 5 + 3 + 2 = 180,

which simplifies to:

6x = 180.

Next, solve for x by adding the constants together:

6x - 180 = 0,

thus:

6x = 180,

and dividing both sides by 6 yields:

x = 30.

Now, substitute x back into the expressions for the angles:

1. For the first angle: 3x - 5 = 3(30) - 5 = 90 - 5 = 85 degrees.

2. For the second angle: 2x + 3 = 2(30) + 3 = 60 + 3 =