The sum of the angles in any triangle is always 180°. So, we can write an equation for the three angles:

$(18x - 7) + (12x + 9) + 4x = 180$

Simplify and solve for $x$:

$18x - 7 + 12x + 9 + 4x = 180$ $(18x + 12x + 4x) + (-7 + 9) = 180$ $34x + 2 = 180$ $34x = 180 - 2$ $34x = 178$ $x = \frac{178}{34} = 5.24$

Now, substitute $x = 5.24$ back into the expressions for the angles:

1. First angle: $18x - 7 = 18(5.24) - 7 = 94.32 - 7 = 87.32^\circ$
2. Second angle: $12x + 9 = 12(5.24) + 9 = 62.88 + 9 = 71.88^\circ$
3. Third angle: $4x = 4(5.24) = 20.96^\circ$

The largest angle is 87.32°, which rounds to 87.3°.

Answer: D) 87.3°

Would you like more details on this process? Or have any other questions?

Here are 5 related questions:

1. How can you check that the sum of the angles in a triangle is always 180°?
2. What would happen if the sum of the angles in a triangle didn't add up to 180°?
3. How can the Law of Sines or Law of Cosines be used to find angles in non-right triangles?
4. What other properties of triangles should be kept in mind when solving angle problems?
5. How do you solve angle problems with unknowns in trigonometric equations?

Tip: When solving angle problems, always check that the sum of the angles is consistent with the fundamental properties of triangles.